--------------------------------------
On computing the Mod, 2, of Many Interesting sequences
by Shalosh B. Ekhad
Theorem Number, 1, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 2, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 23, 94, 402, 1779, 8052, 37006, 171932, 805186, 3793572, 17957251,
85323734, 406676976, 1943412483
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 3, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 38, 184, 952, 5084, 27736, 153696, 860960, 4861408, 27616096, 157617904,
903002336, 5189453312, 29901183328
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 4, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 53, 286, 1682, 10099, 62120, 388126, 2451140, 15606970, 99979640,
643535875, 4158061598, 26950603060, 175140491273
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 5, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 23, 94, 392, 1659, 7107, 30734, 133880, 586576, 2582142, 11411371,
50597900, 224986467, 1002867878
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 6, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 38, 196, 1052, 5774, 32146, 180772, 1024256, 5837908, 33433996, 192239854,
1109049320, 6416509142, 37215072638
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 7, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 53, 310, 1892, 11839, 75245, 483326, 3128768, 20375440, 133329110,
875909995, 5773461956, 38163131387, 252880464038
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 8, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 68, 436, 2912, 19974, 139344, 982916, 6989720, 50010292, 359558784,
2595408094, 18796855508, 136519262598, 993947615048
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 9, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 44, 232, 1232, 6704, 36976, 205664, 1151936, 6489088, 36724096, 208635904,
1189162496, 6796807424, 38941961984
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 10, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 59, 358, 2242, 14299, 92360, 602270, 3956252, 26140330, 173541260,
1156667395, 7734994958, 51873729652, 348741401119
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 11, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 74, 496, 3432, 24204, 172944, 1247488, 9064352, 66245152, 486431904,
3585858544, 26521709216, 196715685248, 1462647306144
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 12, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 89, 646, 4802, 36539, 281668, 2192558, 17192420, 135593314, 1074441568,
8547195331, 68217505670, 545999650616, 4380746574869
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 13, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 71, 430, 2672, 17299, 112835, 740926, 4904360, 32649640, 218325230,
1465532875, 9869605436, 66650927815, 451185626366
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 14, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 86, 580, 4092, 29454, 214314, 1574500, 11652224, 86731012, 648619644,
4869770734, 36682896824, 277107171150, 2098432827606
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 15, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 101, 742, 5692, 44279, 348973, 2776302, 22247120, 179305384, 1451969158,
11803779211, 96276318452, 787489979423, 6457021374286
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 16, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 116, 916, 7472, 61894, 519752, 4404292, 37594232, 322745956, 2783809712,
24105317086, 209419347620, 1824503882686, 15934258258496
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 17, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 18, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 48, 231, 1173, 6164, 33183, 181799, 1008957, 5653701, 31912818,
181156776, 1032969564, 5911392015, 33930026163
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 19, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 69, 393, 2343, 14449, 91269, 586497, 3816411, 25066773, 165813189,
1102873209, 7367533839, 49390996521, 332074347189
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 20, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 90, 567, 3753, 25704, 180225, 1285335, 9281709, 67649985, 496555920,
3664741320, 27164429568, 202060317663, 1507366068435
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 21, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 48, 231, 1163, 5984, 31188, 164047, 869097, 4631211, 24797028, 133302156,
719013636, 3889437080, 21091925888
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 22, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 69, 405, 2503, 15919, 103029, 674613, 4454223, 29596473, 197645649,
1325302119, 8917233705, 60174146899, 407079536539
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 23, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 90, 591, 4083, 29064, 210780, 1547695, 11464281, 85477095, 640576170,
4820411220, 36398556756, 275640152992, 2092580941860
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 24, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 111, 789, 5903, 45539, 358221, 2854693, 22958175, 185888637, 1513000371,
12366428919, 101425821669, 834286694783, 6879610345841
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 25, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 75, 465, 2923, 18589, 119619, 777121, 5085651, 33473133, 221347899,
1469414769, 9786831291, 65367631741, 437665012915
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 26, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 96, 663, 4733, 34464, 254355, 1895735, 14235693, 107538705, 816302490,
6221251320, 47574051372, 364849702967, 2805038513231
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 27, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 117, 873, 6783, 53909, 434661, 3540161, 29052459, 239840217, 1989519381,
16569202329, 138455300727, 1160272014989, 9747281151477
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 28, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 138, 1095, 9073, 77044, 664317, 5788519, 50829213, 449013069, 3985601832,
35518288056, 317584289376, 2847755324839, 25598520695623
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 29, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 108, 783, 5643, 41364, 307800, 2311983, 17485065, 132980535, 1016080200,
7793724420, 59975964324, 462830103576, 3580271880048
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 30, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 129, 1005, 7983, 64619, 530001, 4388645, 36608511, 307172637, 2589753741,
21920819919, 186169052241, 1585620914055, 13538300225319
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 31, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 150, 1239, 10563, 91804, 808272, 7184655, 64335993, 579488499,
5244519822, 47652399276, 434422880388, 3971722599360, 36401193762900
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 32, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 171, 1485, 13383, 123039, 1146393, 10784853, 102210255, 974339361,
9332293743, 89738353791, 865787580765, 8376809358771, 81248052512781
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 33, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 34, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 2, 12, 6, 120, 260, 840, 4550, 10416, 50652, 175560, 571164, 2450448,
7979400, 30702672
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 35, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 24, 24, 480, 1120, 6720, 36960, 123648, 814464, 3252480, 16279296,
83026944, 363297792, 1912694784
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 36, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 36, 54, 1080, 2700, 22680, 126630, 553392, 4143636, 18711000, 118713276,
665512848, 3580258968, 21938572656
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 37, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 3, 24, 40, 175, 420, 1456, 4116, 13104, 39600, 122991, 380952, 1180036,
3686683
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 38, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 15, 78, 350, 1515, 7350, 32942, 157920, 734706, 3498000, 16578771,
79073280, 377947856, 1810383575
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 39, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 27, 144, 900, 4175, 26460, 136640, 805140, 4489128, 25678620, 147274479,
842037768, 4863568424, 27995674707
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 40, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 39, 222, 1690, 8275, 62790, 355390, 2408952, 15154650, 97837740,
638712195, 4112747496, 26998857028, 175518862519
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 41, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 12, 96, 320, 1520, 6720, 28672, 134400, 580608, 2703360, 12021504,
55351296, 250984448, 1151101952
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 42, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 24, 198, 880, 5380, 28560, 164934, 924000, 5303340, 30299280, 174574620,
1006825248, 5829520840, 33815445664
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 43, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 36, 312, 1680, 11280, 70560, 458080, 2975616, 19418112, 127670400,
840390144, 5560828416, 36850418176, 244984836096
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 44, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 48, 438, 2720, 19340, 137760, 964390, 7017024, 50038884, 364980000,
2642109756, 19317355200, 141107646680, 1035194608448
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 45, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 27, 216, 1080, 5535, 34020, 172368, 1041012, 5633712, 32717520,
184926159, 1058315544, 6083437932, 34854046227
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 46, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 39, 366, 1950, 13355, 84630, 555086, 3660384, 24151554, 160995120,
1072726611, 7191385344, 48262029816, 324988783119
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 47, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 16, 51, 528, 3060, 23935, 164220, 1219680, 8809332, 65106216, 479262300,
3556725711, 26425456200, 197088262800, 1472727467211
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 48, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 63, 702, 4410, 37395, 277830, 2235870, 17495352, 140056938, 1117046700,
8979363459, 72278197992, 583933176684, 4727043624303
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 49, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 50, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 3, 19, 67, 291, 1341, 5853, 26419, 120403, 547993, 2513193, 11570989,
53408941, 247299027, 1147809939
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 51, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 37, 145, 881, 4901, 26405, 152097, 857953, 4884805, 28079525, 161316145,
931359313, 5392226789, 31279571237
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 52, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 55, 235, 1771, 10801, 67537, 450115, 2882467, 18952597, 124876357,
822501109, 5456962837, 36235266991, 241267084975
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 53, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 16, 61, 231, 896, 3515, 13917, 55501, 222595, 896930, 3628120, 14724022,
59922175, 244456581
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 54, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 34, 175, 951, 5176, 28687, 160231, 901663, 5103097, 29016472, 165634624,
948599692, 5447994839, 31365144909
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 55, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 52, 301, 1971, 12396, 80739, 527437, 3472261, 23001919, 153016194,
1022072536, 6848799010, 46022234519, 310008304797
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 56, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 70, 439, 3291, 22676, 165551, 1202055, 8807551, 64986901, 481075376,
3577692856, 26685660496, 199616797615, 1496806789125
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 57, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 37, 193, 1001, 5241, 28029, 150529, 815761, 4443049, 24314709, 133573441,
736168057, 4068611353, 22540316717
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 58, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 55, 355, 2211, 14261, 92681, 608819, 4026691, 26789041, 179056901,
1201500301, 8088847261, 54610234459, 369590414295
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 59, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 73, 529, 3721, 26941, 197233, 1456673, 10840465, 81117613, 609893593,
4603215409, 34857719833, 264699597917, 2014944995713
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 60, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 91, 715, 5531, 43401, 347565, 2794051, 22682899, 184983085, 1516274145,
12474913045, 102976097173, 852405168343, 7073074138691
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 61, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 64, 397, 2551, 15976, 104203, 676957, 4447981, 29366443, 194743858,
1296733384, 8661154438, 58014153679, 389517227749
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 62, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 82, 607, 4311, 31536, 233535, 1743463, 13120255, 99267985, 754699320,
5759824720, 44104291180, 338667328455, 2606900765757
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 63, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 100, 829, 6371, 51476, 416627, 3415245, 28165861, 233706727, 1948038962,
16301553544, 136861333714, 1152270624935, 9724867347485
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 64, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 118, 1063, 8731, 75916, 659359, 5805703, 51411295, 458084269, 4100076784,
36841864456, 332129714320, 3002567395231, 27210163458133
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 65, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 66, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 32, 166, 852, 4524, 24432, 132934, 728348, 4014676, 22233312, 123605596,
689449256, 3856481880, 21624138912
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 67, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 56, 328, 2032, 13184, 85696, 562272, 3721664, 24763648, 165534976,
1110924544, 7479881216, 50503294976, 341822273536
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 68, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 80, 502, 3572, 26164, 190640, 1411750, 10529756, 78907660, 594342080,
4493839420, 34087429352, 259297309288, 1977203630240
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 69, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 35, 160, 752, 3599, 17446, 85376, 420884, 2087008, 10398016, 52010479,
261021854, 1313707256, 6628095035
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 70, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 59, 358, 2242, 14299, 92360, 602270, 3956252, 26140330, 173541260,
1156667395, 7734994958, 51873729652, 348741401119
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 71, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 83, 568, 4092, 29919, 221454, 1655056, 12458036, 94317592, 717428604,
5478493519, 41973619118, 322490785244, 2483811265323
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 72, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 107, 790, 6302, 50579, 411448, 3380654, 27966932, 232713394, 1945471288,
16327320211, 137477812214, 1160835229064, 9825733252727
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 73, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 68, 400, 2432, 15024, 93984, 593408, 3773696, 24136192, 155096064,
1000509184, 6475410944, 42027531264, 273436525568
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 74, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 92, 646, 4652, 34124, 253528, 1901638, 14368844, 109208164, 833981128,
6394017436, 49185717752, 379438594136, 2934361958192
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 75, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 116, 904, 7232, 58864, 485312, 4038752, 33856064, 285456256, 2418204032,
20565984256, 175486400000, 1501643090432, 12881109687296
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 76, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 140, 1174, 10172, 89364, 796056, 7155110, 64782572, 589921948,
5397220776, 49572508924, 456817283288, 4221516171240, 39106924773680
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 77, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 107, 736, 5312, 38719, 286022, 2132512, 16011188, 120903136, 917200352,
6985016911, 53368875614, 408904516960, 3140554335587
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 78, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 131, 1030, 8322, 68379, 569256, 4783678, 40494812, 344797498, 2949775116,
25335206659, 218324891150, 1886757094044, 16345408354311
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 79, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 20, 155, 1336, 11692, 104399, 943630, 8610480, 79141844, 731648920,
6795953980, 63372712495, 592914790574, 5563039388612, 52323374287315
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 80, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 179, 1654, 15422, 146899, 1415864, 13776718, 135021140, 1330957762,
13181632664, 131060482579, 1307396822006, 13078832786608, 131156898478559
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 81, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 82, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 57, 339, 2073, 12869, 81063, 516371, 3315513, 21415761, 138994683,
905707581, 5921485911, 38825170731, 255192103017
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 83, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 87, 609, 4323, 31549, 234279, 1757121, 13276995, 100922733, 770828919,
5910673569, 45473210019, 350836300317, 2713419535047
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 84, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 117, 891, 6993, 56889, 469395, 3909411, 32816745, 277120845, 2351230335,
20027470725, 171156328047, 1466848379655, 12601932138477
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 85, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 66, 357, 1993, 11344, 65439, 381229, 2237799, 13214763, 78417144,
467210544, 2793104694, 16746295159, 100655033791
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 86, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 96, 663, 4733, 34464, 254355, 1895735, 14235693, 107538705, 816302490,
6221251320, 47574051372, 364849702967, 2805038513231
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 87, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 126, 981, 7893, 64844, 539871, 4538333, 38433663, 327393927, 2802193056,
24079196304, 207602903394, 1794990074783, 15558234035031
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 88, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 156, 1311, 11473, 102604, 929547, 8503063, 78356685, 726274989,
6763643802, 63236216976, 593184569760, 5580127723231, 52621419169831
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 89, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 111, 753, 5243, 37169, 266871, 1934305, 14122803, 103715217, 765283071,
5669058129, 42134877099, 314054824625, 2346580226951
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 90, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 141, 1107, 8953, 73789, 616227, 5196627, 44152809, 377379369, 3241135527,
27948336381, 241813226151, 2098240353907, 18252025766941
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 91, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 171, 1473, 13083, 118389, 1085283, 10044673, 93656115, 878386581,
8277708123, 78317021121, 743453353035, 7077691236469, 67546304093331
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 92, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 201, 1851, 17633, 171089, 1681599, 16685923, 166785177, 1676848293,
16939092459, 171789670149, 1748022315471, 17837360202671, 182465597624561
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 93, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 162, 1269, 10233, 84024, 698463, 5860269, 49524615, 420938451,
3594605688, 30815984736, 265051212390, 2286157926087, 19766997379647
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 94, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 192, 1671, 14973, 136664, 1263699, 11798327, 110974989, 1050011433,
9982721994, 95287086024, 912593172780, 8765282582247, 84397758645087
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 95, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 222, 2085, 20133, 198004, 1972575, 19840221, 201031647, 2048944815,
20983122240, 215740158720, 2225578627314, 23024747205807, 238791366352887
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 96, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 252, 2511, 25713, 268164, 2832651, 30206871, 324489645, 3506130117,
38064293226, 414877585824, 4536977899392, 49756312005903, 547012699861527
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 97, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 98, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 2, 27, 6, 270, 1235, 1890, 22750, 72576, 255402, 1746360, 5493939, 26594568,
135246540, 485431947
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 99, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 54, 24, 1080, 5020, 15120, 182560, 671328, 4090464, 28939680, 123872496,
861404544, 4873083072, 25497055584
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 100, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 81, 54, 2430, 11475, 51030, 618030, 2571912, 20728386, 151559100,
809349651, 6620101488, 41146707888, 270064675881
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 101, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 3, 54, 60, 555, 945, 6174, 13692, 72576, 191070, 887931, 2617758,
11184459, 35543508
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 102, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 30, 132, 900, 3950, 24150, 126308, 701400, 3925908, 21624900, 121975854,
681415020, 3840592470, 21661690050
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 103, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 57, 222, 2280, 10975, 81795, 530670, 3381924, 23536800, 152618070,
1039404795, 6982162902, 47006723907, 319562335092
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 104, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 84, 324, 4200, 21750, 185220, 1378020, 9654960, 77517972, 560138040,
4319736894, 32810561784, 248190577206, 1910801416524
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 105, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 12, 216, 480, 4560, 15120, 106848, 440832, 2685312, 12481920, 70608384,
349899264, 1910168832, 9793335552
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 106, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 39, 366, 1950, 13355, 84630, 555086, 3660384, 24151554, 160995120,
1072726611, 7191385344, 48262029816, 324988783119
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 107, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 16, 66, 528, 3960, 26860, 212520, 1525440, 11760672, 88202016, 674018400,
5147940336, 39453860160, 303552300480, 2338399199136
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 108, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 93, 702, 6510, 45195, 410130, 3196830, 27180552, 225560538, 1888355700,
15956447859, 134330645592, 1140101509404, 9668650244253
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 109, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 27, 486, 1620, 15795, 76545, 581742, 3367980, 23147208, 145063710,
961967259, 6231677166, 40944989943, 268823406852
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 110, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 20, 54, 708, 3780, 33230, 224910, 1780324, 13086360, 101075940, 765885780,
5900921070, 45300140028, 350025900510, 2705769780714
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 111, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 22, 81, 942, 6480, 56455, 456435, 3829630, 32176116, 271455912, 2307734550,
19643430939, 168054990246, 1440139057071, 12379261890996
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 112, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 24, 108, 1188, 9720, 85590, 782460, 6928740, 63930384, 579843684, 5355088200,
49289858046, 456764485320, 4238037731070, 39439963911348
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 113, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 114, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 3, 34, 127, 591, 3516, 17403, 89559, 486223, 2563693, 13626768, 73395664,
394170076, 2123218527, 11485869489
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 115, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 67, 265, 1781, 13001, 75755, 509377, 3424153, 22171405, 148805075,
996671545, 6649852093, 44795141249, 301849584587
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 116, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 100, 415, 3571, 28576, 187237, 1492135, 11255167, 83425897, 646296982,
4920865984, 37636345072, 290615028991, 2236998217825
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 117, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 22, 103, 421, 1876, 8212, 36751, 164731, 744367, 3375802, 15375724,
70247932, 321870472, 1478312752
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 118, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 55, 301, 1941, 12051, 76539, 491653, 3172213, 20609749, 134486859,
880976911, 5790193891, 38161698927, 252127029345
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 119, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 88, 511, 4061, 29276, 216476, 1639023, 12344875, 93984811, 718288616,
5507806756, 42393510940, 327138855824, 2530654004708
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 120, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 121, 733, 6781, 53671, 440203, 3731701, 31129573, 264009433, 2244464773,
19134087919, 163865679199, 1406297414731, 12100128720511
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 121, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 49, 337, 1801, 11101, 65353, 398497, 2418961, 14842093, 91288033,
564173809, 3496652953, 21735716029, 135429712249
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 122, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 82, 607, 4311, 31536, 233535, 1743463, 13120255, 99267985, 754699320,
5759824720, 44104291180, 338667328455, 2606900765757
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 123, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 115, 889, 7421, 60101, 504827, 4240545, 35968201, 306713977, 2627331587,
22596482569, 194964688309, 1686946101725, 14631750660635
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 124, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 148, 1183, 11131, 96916, 891409, 8162743, 75430255, 701729869,
6551407534, 61437972256, 577905187120, 5451487479751, 51549534477733
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 125, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 82, 703, 4501, 33616, 239464, 1763119, 12954331, 96022099, 714380734,
5336114356, 39990027052, 300504579688, 2263719904192
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 126, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 21, 115, 1045, 8061, 67911, 563991, 4774869, 40568101, 347130241, 2982786951,
25735012711, 222755304331, 1933596302379, 16825136788845
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 127, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 23, 148, 1399, 12221, 111416, 1023968, 9495823, 88759435, 834019663,
7875349868, 74646026764, 709883092348, 6769870809872, 64719048195188
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 128, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 181, 1765, 16981, 164251, 1631575, 16219141, 163031509, 1645522885,
16695438145, 170022115495, 1737195291703, 17799551994823, 182818704607291
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 129, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 130, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 47, 286, 1602, 9699, 60132, 371214, 2307548, 14462626, 91035012,
574991971, 3644088086, 23160978000, 147557748987
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 131, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 86, 568, 3832, 29084, 215896, 1601632, 12091424, 91668448, 696993376,
5324668144, 40813043936, 313636507136, 2416170403936
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 132, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 125, 862, 6722, 58339, 480440, 4024990, 34336196, 292592410, 2506012280,
21575034595, 186221653022, 1611833827348, 13987050486065
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 133, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 47, 238, 1232, 6499, 34715, 187198, 1016840, 5555560, 30497150,
168073195, 929348396, 5153362231, 28646281502
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 134, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 86, 580, 4092, 29454, 214314, 1574500, 11652224, 86731012, 648619644,
4869770734, 36682896824, 277107171150, 2098432827606
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 135, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 125, 934, 7612, 63239, 527893, 4458990, 37932272, 324456424, 2788550998,
24059445931, 208264503332, 1807870237775, 15731693608750
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 136, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 164, 1300, 11792, 107974, 988472, 9194308, 86027960, 809204836,
7649884112, 72591979486, 691100890820, 6598091552446, 63145950761744
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 137, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 92, 616, 4112, 28144, 194672, 1359712, 9564608, 67668736, 480993152,
3432257536, 24572409344, 176415489280, 1269645293312
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 138, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 131, 1030, 8322, 68379, 569256, 4783678, 40494812, 344797498, 2949775116,
25335206659, 218324891150, 1886757094044, 16345408354311
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 139, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 20, 170, 1456, 13192, 120524, 1116880, 10446720, 98412704, 932492320,
8877227680, 84841358320, 813525505184, 7822772575232, 75406885390240
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 140, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 209, 1894, 18722, 184699, 1850564, 18722638, 190691300, 1953749362,
20110451264, 207809229379, 2154452620166, 22399057482208, 233442446848109
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 141, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 143, 1150, 9032, 73099, 597179, 4926478, 40930136, 341993392, 2870906414,
24193487179, 204549937724, 1734265825699, 14739563348918
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 142, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 24, 182, 1636, 14652, 134574, 1249698, 11719908, 110707904, 1051886164,
10041899628, 96243953326, 925494049352, 8924981592726, 86279519856942
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 143, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 26, 221, 2134, 20932, 209039, 2115157, 21598462, 222173024, 2298591856,
23893662982, 249347367691, 2610737565620, 27412590681467, 288535722978646
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 144, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 28, 260, 2644, 27872, 296614, 3206576, 34956100, 383915672, 4240653748,
47061843776, 524325629854, 5860892884628, 65697830284870, 738240048624680
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 145, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 146, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 72, 519, 3573, 24644, 173463, 1236391, 8870013, 63965061, 463456458,
3371364456, 24605785116, 180089790591, 1321295828067
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 147, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 117, 969, 7623, 62449, 523029, 4402561, 37283355, 317766933, 2721298869,
23392826169, 201748806639, 1744882927017, 15127859195397
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 148, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 162, 1431, 12393, 114264, 1064745, 9946071, 93723885, 888873345,
8466051960, 80944806600, 776511880992, 7470005128335, 72034992484227
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 149, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 84, 495, 3003, 18564, 116280, 735471, 4686825, 30045015, 193536720,
1251677700, 8122425444, 52860229080, 344867425584
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 150, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 129, 1005, 7983, 64619, 530001, 4388645, 36608511, 307172637, 2589753741,
21920819919, 186169052241, 1585620914055, 13538300225319
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 151, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 174, 1527, 13683, 125644, 1167792, 10951887, 103467225, 983191059,
9386847462, 89971525356, 865223993988, 8344144919808, 80667564994164
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 152, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 219, 2061, 20103, 201759, 2043513, 20886357, 215095503, 2227784481,
23181720543, 242168099391, 2538160889085, 26677526149491, 281081075987229
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 153, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 147, 1089, 8283, 64149, 503163, 3984129, 31778355, 254950101, 2055118563,
16631351361, 135039238155, 1099575642837, 8975450076747
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 154, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 192, 1671, 14973, 136664, 1263699, 11798327, 110974989, 1050011433,
9982721994, 95287086024, 912593172780, 8765282582247, 84397758645087
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 155, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 237, 2265, 22383, 225229, 2294925, 23607201, 244625547, 2549708865,
26701907565, 280741645545, 2961531192519, 31330045673637, 332256772573437
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 156, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 282, 2871, 30513, 329964, 3610701, 39892071, 443946045, 4969177317,
55884278376, 630954015624, 7147318455072, 81192874716183, 924604690710327
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 157, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 216, 1863, 16443, 147744, 1344276, 12345615, 114202953, 1062534267,
9932277996, 93207429324, 877574192004, 8285942274840, 78425918957376
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 158, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 29, 261, 2517, 24903, 251039, 2563557, 26431477, 274548879, 2868644169,
30117280977, 317454892071, 3357408221001, 35609843787267, 378626397171291
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 159, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 31, 306, 3183, 34083, 371464, 4100988, 45707503, 513189945, 5795720631,
65766426498, 749233731156, 8564024112660, 98169292496544, 1128088286442756
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 160, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 33, 351, 3861, 43983, 509139, 5970429, 70675173, 842740767, 10107524493,
121801153059, 1473552741879, 17886314377701, 217724895110511,
2656812164068161
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 161, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 162, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 3, 24, 60, 175, 840, 1680, 10164, 20664, 115500, 281391, 1297296, 3838692,
14897883
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 163, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 6, 96, 240, 1340, 6720, 22400, 161952, 459648, 3622080, 10888944,
78414336, 272638080, 1691385696
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 164, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 9, 216, 540, 4455, 22680, 105840, 818748, 2980152, 27318060, 97037919,
875674800, 3421386540, 27672053409
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 165, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 2, 6, 6, 40, 80, 210, 742, 1680, 5292, 15180, 40524, 123552, 343772, 986986
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 166, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 9, 78, 240, 1335, 5355, 26110, 115668, 543816, 2499750, 11680251,
54478710, 255144175, 1198160964
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 167, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 12, 198, 560, 5020, 20580, 144774, 708960, 4486860, 23980440, 144874620,
809018496, 4792044400, 27372997652
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 168, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 15, 366, 1000, 12095, 50925, 454174, 2386860, 18396504, 108650850,
779959851, 4901037570, 34002807839, 220881360700
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 169, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 24, 24, 320, 1120, 3360, 22624, 75264, 330624, 1647360, 6141696, 28993536,
128567296, 531474944
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 170, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 27, 144, 900, 4175, 26460, 136640, 805140, 4489128, 25678620, 147274479,
842037768, 4863568424, 27995674707
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 171, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 30, 312, 1600, 11100, 71400, 458528, 3108000, 20083392, 136646400,
899829744, 6102233280, 40770878720, 276156680800
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 172, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 16, 33, 528, 2420, 22855, 143220, 1139488, 8072988, 60993576, 452043900,
3381052191, 25456211352, 190893946672, 1445604273113
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 173, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 54, 54, 1080, 5400, 17010, 168966, 734832, 3735396, 26462700, 121920876,
720555264, 4342096044, 22027599594
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 174, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 57, 222, 2280, 10975, 81795, 530670, 3381924, 23536800, 152618070,
1039404795, 6982162902, 47006723907, 319562335092
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 175, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 60, 438, 3600, 21860, 186900, 1255142, 9935520, 72688644, 553179000,
4194002076, 31747510080, 243010832064, 1850355807300
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 176, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 63, 702, 5040, 39015, 337365, 2547342, 22210524, 174808368, 1491453810,
12159698859, 102397032738, 851248720179, 7145398368108
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 177, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 178, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 16, 61, 251, 1016, 4355, 18621, 81205, 356155, 1573430, 6986200, 31140994,
139281455, 624616361
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 179, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 31, 169, 861, 4461, 24879, 134401, 761161, 4256689, 24262239, 138207961,
792787477, 4559039109, 26298912831
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 180, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 46, 325, 1831, 11296, 73333, 458221, 3058453, 19770643, 132459988,
876676384, 5889337390, 39487679167, 266278586041
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 181, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 3, 13, 43, 151, 561, 2073, 7715, 29011, 109633, 416043, 1585189, 6059353,
23224995, 89233693
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 182, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 28, 151, 781, 4216, 22912, 125903, 696619, 3876607, 21673972, 121646284,
684987772, 3867943184, 21894249748
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 183, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 43, 307, 1771, 11741, 75041, 496147, 3271363, 21799681, 145653641,
977889661, 6584131477, 44463245243, 300965380363
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 184, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 58, 511, 3121, 24096, 170220, 1283087, 9497587, 71685175, 540207570,
4100350420, 31177505308, 237913339392, 1819227859828
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 185, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 37, 145, 721, 3941, 19685, 101921, 539425, 2828485, 14942885, 79455025,
422942833, 2258151845, 12090801637
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 186, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 52, 301, 1971, 12396, 80739, 527437, 3472261, 23001919, 153016194,
1022072536, 6848799010, 46022234519, 310008304797
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 187, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 67, 505, 3581, 26161, 194923, 1453985, 10981417, 83169013, 633698803,
4844056009, 37158496597, 285810497545, 2203736079467
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 188, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 82, 757, 5551, 46196, 373997, 3099965, 25778917, 215711767, 1814123312,
15307993504, 129640671694, 1100704760039, 9369279969157
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 189, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 73, 307, 1951, 13861, 81397, 523699, 3469123, 22152637, 144481327,
950666509, 6220704673, 40951593151, 270535280113
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 190, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 88, 511, 4061, 29276, 216476, 1639023, 12344875, 93984811, 718288616,
5507806756, 42393510940, 327138855824, 2530654004708
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 191, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 103, 763, 6531, 51441, 433245, 3598435, 30310771, 256550845, 2179900845,
18608015845, 159288912589, 1367623508343, 11769778788783
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 192, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 118, 1063, 9361, 81316, 743464, 6674095, 61288435, 561646819, 5188163014,
48049343596, 446613538060, 4162613091040, 38889202725028
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 193, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 194, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 35, 160, 772, 3839, 19546, 101280, 531764, 2820328, 15075436, 81076879,
438164534, 2377297784, 12939840475
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 195, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 62, 352, 2112, 12924, 81384, 520384, 3373856, 22095232, 145856064,
968879344, 6468148832, 43355525568, 291572336352
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 196, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 89, 592, 4052, 28279, 204122, 1489408, 11047292, 82683016, 624138572,
4740876991, 36196764086, 277510473088, 2134831686929
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 197, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 26, 118, 532, 2424, 11202, 52294, 245852, 1162276, 5520132, 26318956,
125894264, 603888172, 2903740306
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 198, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 53, 310, 1892, 11839, 75245, 483326, 3128768, 20375440, 133329110,
875909995, 5773461956, 38163131387, 252880464038
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 199, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 80, 550, 3852, 28004, 206908, 1548614, 11690252, 88826884, 678354448,
5201650876, 40021385432, 308804317696, 2388582610260
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 200, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 107, 838, 6412, 51879, 424671, 3533758, 29660408, 250787968, 2131747026,
18198477499, 155900165072, 1339453334587, 11536897514542
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 201, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 56, 328, 1872, 11264, 68896, 422496, 2608832, 16215808, 101245696,
634457344, 3988795904, 25147276288, 158919553536
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 202, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 83, 568, 4092, 29919, 221454, 1655056, 12458036, 94317592, 717428604,
5478493519, 41973619118, 322490785244, 2483811265323
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 203, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 110, 856, 6912, 56764, 473552, 3985888, 33802976, 288314176, 2470687232,
21254884336, 183453431072, 1587863444288, 13777051707360
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 204, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 20, 137, 1192, 10332, 92759, 843670, 7754352, 71825276, 669148600,
6263877820, 58863975295, 554990112926, 5247322710244, 49732947077217
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 205, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 98, 646, 4292, 31744, 232850, 1698022, 12567932, 93653980, 699652340,
5247942220, 39505205144, 298161175420, 2255610249458
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 206, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 125, 934, 7612, 63239, 527893, 4458990, 37932272, 324456424, 2788550998,
24059445931, 208264503332, 1807870237775, 15731693608750
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 207, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 152, 1270, 11532, 104364, 961116, 8930086, 83542796, 786199228,
7432817856, 70545012124, 671743016024, 6414432545616, 61400028720612
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 208, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 179, 1654, 16052, 156079, 1550999, 15504430, 156274568, 1583754712,
16125974834, 164835049339, 1690401666800, 17383950058063, 179208657048374
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 209, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 210, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 66, 357, 2013, 11704, 69639, 421773, 2590095, 16080003, 100696764,
634971984, 4026467682, 25649269239, 164004740211
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 211, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 105, 681, 4623, 32309, 230961, 1680065, 12388875, 92345337, 694259481,
5255535129, 40006451943, 305926461837, 2348176521105
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 212, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 144, 1053, 8073, 63504, 511353, 4187997, 34769007, 291769371, 2469513258,
21046597416, 180378463086, 1553020693623, 13421838407859
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 213, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 51, 267, 1453, 8009, 44523, 249475, 1407705, 7989561, 45561453,
260841381, 1498267683, 8630351531, 49834369891
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 214, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 90, 591, 4083, 29064, 210780, 1547695, 11464281, 85477095, 640576170,
4820411220, 36398556756, 275640152992, 2092580941860
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 215, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 129, 963, 7553, 61189, 506187, 4247091, 35990697, 307223289, 2637127947,
22735986381, 196719062751, 1707147542707, 14852303960369
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 216, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 168, 1383, 11863, 105344, 955944, 8807983, 82033377, 770071743,
7272174264, 68995741164, 657063780948, 6276730763312, 60115676023108
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 217, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 87, 609, 4163, 28669, 200679, 1420225, 10119939, 72497133, 521739639,
3769359009, 27320908995, 198577505629, 1446808589447
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 218, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 126, 981, 7893, 64844, 539871, 4538333, 38433663, 327393927, 2802193056,
24079196304, 207602903394, 1794990074783, 15558234035031
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 219, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 165, 1401, 12463, 113529, 1050213, 9817313, 92480619, 876391101,
8344970373, 79774962441, 765156914343, 7359792205073, 70965068021365
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 220, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 204, 1869, 17873, 175684, 1756905, 17771245, 181242591, 1859938335,
19180826910, 198596982120, 2063136787182, 21493951800031, 224474815572719
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 221, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 135, 1107, 8613, 69309, 571455, 4741011, 39530025, 331582005, 2794975065,
23647888845, 200717858331, 1708381779399, 14575656833055
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 222, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 174, 1527, 13683, 125644, 1167792, 10951887, 103467225, 983191059,
9386847462, 89971525356, 865223993988, 8344144919808, 80667564994164
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 223, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 213, 1995, 19593, 195929, 1983999, 20284931, 208906809, 2163923253,
22520484759, 235295215989, 2466511223751, 25928668096431, 273236607114813
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 224, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 252, 2511, 26343, 281124, 3045276, 33307983, 367007841, 4067511147,
45292539636, 506315837124, 5678678950740, 63870003270576, 720120739050612
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 225, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 226, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 25, 97, 521, 2501, 12545, 64065, 325393, 1674565, 8636585, 44720545,
232429081, 1210941317, 6325164305
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 227, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 49, 241, 1761, 10041, 67089, 429409, 2785729, 18358249, 120259569,
796268881, 5272973473, 35045465625, 233510713809
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 228, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 73, 433, 3721, 23581, 190513, 1378273, 10517905, 80210413, 609407833,
4698123409, 36048870937, 278629449853, 2154641061313
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 229, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 19, 73, 301, 1241, 5195, 21953, 93385, 399565, 1717475, 7410745, 32080933,
139264529, 606012139
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 230, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 43, 265, 1581, 9741, 60579, 380353, 2405545, 15299089, 97761819,
627109561, 4035938245, 26047182149, 168512126883
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 231, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 67, 505, 3581, 26161, 194923, 1453985, 10981417, 83169013, 633698803,
4844056009, 37158496597, 285810497545, 2203736079467
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 232, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 91, 793, 6301, 51461, 435107, 3632609, 31014217, 263924857, 2266951787,
19502967529, 168496623829, 1459244026397, 12669561636931
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 233, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 49, 241, 1441, 8121, 46929, 275297, 1616449, 9568489, 56878449, 339316561,
2031216097, 12191914905, 73355518609
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 234, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 73, 529, 3721, 26941, 197233, 1456673, 10840465, 81117613, 609893593,
4603215409, 34857719833, 264699597917, 2014944995713
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 235, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 97, 865, 6721, 56561, 470177, 3982273, 33843841, 289684177, 2489672417,
21484861729, 185996101825, 1614743032241, 14052331289377
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 236, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 21, 121, 1249, 10441, 97941, 892641, 8349377, 78118033, 737035861,
6978684681, 66360270241, 632981525593, 6054915252309, 58058495769841
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 237, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 91, 505, 3901, 26641, 187363, 1358113, 9730153, 70618933, 514644043,
3759227209, 27578274517, 202798937641, 1494850486051
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 238, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 115, 889, 7421, 60101, 504827, 4240545, 35968201, 306713977, 2627331587,
22596482569, 194964688309, 1686946101725, 14631750660635
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 239, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 21, 139, 1321, 11661, 107241, 995331, 9311233, 87855817, 832941661,
7937381211, 75914930521, 728509774981, 7010399216289, 67625067981219
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 240, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 163, 1801, 16621, 169021, 1685755, 17174977, 175424617, 1805017825,
18647693395, 193433769145, 2012924810053, 21005971610677, 219738531772603
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 241, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 242, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 75, 465, 3003, 20029, 136419, 941985, 6567411, 46113453, 325553979,
2308301169, 16424559531, 117213313629, 838596904275
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 243, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 123, 897, 6963, 55889, 457131, 3791489, 31753059, 267811857, 2271082971,
19342185729, 165311886483, 1417029334353, 12177024531723
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 244, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 171, 1377, 12123, 109269, 1004643, 9374913, 88309683, 837885141,
7993601883, 76590962721, 736454791179, 7102209714453, 68664009249171
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 245, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 69, 393, 2303, 13729, 82869, 504961, 3099723, 19139733, 118747269,
739662009, 4622692311, 28973271193, 182042465189
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 246, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 117, 873, 6783, 53909, 434661, 3540161, 29052459, 239840217, 1989519381,
16569202329, 138455300727, 1160272014989, 9747281151477
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 247, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 165, 1401, 12463, 113529, 1050213, 9817313, 92480619, 876391101,
8344970373, 79774962441, 765156914343, 7359792205073, 70965068021365
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 248, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 213, 1977, 19343, 193549, 1969845, 20263777, 210108939, 2191759425,
22973774805, 241762494345, 2552615050599, 27027715134949, 286875624839333
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 249, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 123, 897, 6643, 50129, 383211, 2956417, 22971363, 179511057, 1409365851,
11108173569, 87838769619, 696545218001, 5536916176843
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 250, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 171, 1473, 13083, 118389, 1085283, 10044673, 93656115, 878386581,
8277708123, 78317021121, 743453353035, 7077691236469, 67546304093331
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 251, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 219, 2097, 20723, 208969, 2135115, 22025313, 228879075, 2392300665,
25123555515, 264882406545, 2801979624915, 29724048024745, 316093568851499
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 252, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 29, 267, 2769, 29563, 322829, 3573027, 39933217, 449598579, 5091390909,
57928915707, 661687723761, 7583049315819, 87148577826605, 1004007555520147
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 253, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 189, 1593, 13743, 121689, 1089693, 9840609, 89511723, 818863101,
7525639773, 69429995721, 642636244071, 5964774222897, 55497229084269
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 254, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 237, 2265, 22383, 225229, 2294925, 23607201, 244625547, 2549708865,
26701907565, 280741645545, 2961531192519, 31330045673637, 332256772573437
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 255, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 29, 285, 2985, 32223, 353969, 3938637, 44239169, 500533323, 5696099109,
65129071197, 747614001561, 8610311984823, 99446801724201, 1151402024923965
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 256, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 33, 333, 3753, 43263, 508869, 6061149, 72878913, 882668907, 10752276393,
131597190189, 1616928532569, 19932804539703, 246417800073597,
3053770977909933
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 257, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 258, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 27, 24, 540, 1375, 7560, 46480, 151956, 1028664, 4365900, 21269391,
115459344, 509303652, 2732997267
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 259, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 54, 96, 2160, 6140, 60480, 380800, 1941408, 16587648, 85821120, 630549744,
4026806784, 25057718400, 175879607904
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 260, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 81, 216, 4860, 15255, 204120, 1315440, 9001692, 84628152, 515300940,
4671075519, 33100507440, 257016808620, 2057492077641
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 261, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 6, 54, 120, 600, 1890, 7686, 27888, 106596, 405900, 1536876, 5930496,
22580844, 87393306
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 262, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 33, 222, 1320, 7375, 47355, 275310, 1736196, 10533600, 65706630,
407151195, 2540530278, 15886755027, 99530939508
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 263, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 60, 438, 3600, 21860, 186900, 1255142, 9935520, 72688644, 553179000,
4194002076, 31747510080, 243010832064, 1850355807300
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 264, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 87, 702, 6960, 45015, 465885, 3420942, 31646076, 260992368, 2266338690,
19641326859, 168546711762, 1476712358979, 12765083222892
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 265, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 24, 216, 960, 5280, 30240, 155232, 913920, 4862592, 28005120, 154623744,
877713408, 4942958592, 27981617664
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 266, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 16, 51, 528, 3060, 23935, 164220, 1219680, 8809332, 65106216, 479262300,
3556725711, 26425456200, 197088262800, 1472727467211
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 267, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 20, 78, 888, 6240, 54620, 447720, 3783584, 32192160, 273792960, 2354626560,
20223463920, 174881513664, 1513047169920, 13140216337248
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 268, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 24, 105, 1296, 10500, 98295, 926100, 8481984, 81711420, 763585704,
7355432700, 69944084991, 674045812440, 6476674525464, 62569963481025
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 269, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 54, 486, 3240, 19440, 153090, 949158, 7103376, 47947788, 342090540,
2413686924, 17023118112, 121627476828, 862150002714
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 270, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 22, 81, 942, 6480, 56455, 456435, 3829630, 32176116, 271455912, 2307734550,
19643430939, 168054990246, 1440139057071, 12379261890996
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 271, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 26, 108, 1446, 10800, 109820, 971460, 9359686, 87327072, 835927596,
7957022040, 76432242876, 734600161152, 7089753603504, 68541504539508
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 272, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 30, 135, 1998, 16200, 180495, 1743525, 18335646, 187075980, 1954040760,
20334179250, 213218995275, 2239378803090, 23600482604127, 249264553437900
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 273, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 274, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 40, 157, 971, 5576, 30395, 179005, 1031413, 5980315, 35100110, 205693720,
1211220466, 7155115007, 42338723705
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 275, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 79, 361, 3261, 21741, 154239, 1167489, 8350729, 62256049, 461728719,
3426137881, 25657449013, 191916851205, 1441012522959
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 276, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 118, 613, 6871, 49456, 423613, 3667693, 30117205, 262818163, 2235089308,
19251393184, 166733675902, 1440502088143, 12526084088713
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 277, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 25, 115, 511, 2341, 10837, 50611, 238147, 1126717, 5355967, 25557709,
122356417, 587411839, 2826889345
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 278, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 64, 415, 2861, 19436, 135836, 952239, 6735691, 47899531, 342216656,
2454572836, 17662711132, 127456452176, 921970893764
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 279, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 103, 763, 6531, 51441, 433245, 3598435, 30310771, 256550845, 2179900845,
18608015845, 159288912589, 1367623508343, 11769778788783
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 280, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 142, 1159, 11521, 99316, 955144, 8852719, 83961043, 798667459,
7620245854, 73134845356, 703218082828, 6785305011616, 65610936999172
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 281, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 61, 385, 2401, 14941, 96013, 615553, 3993793, 26015533, 170310493,
1119220609, 7378509217, 48780642301, 323266358701
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 282, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 100, 829, 6371, 51476, 416627, 3415245, 28165861, 233706727, 1948038962,
16301553544, 136861333714, 1152270624935, 9724867347485
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 283, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 21, 139, 1321, 11661, 107241, 995331, 9311233, 87855817, 832941661,
7937381211, 75914930521, 728509774981, 7010399216289, 67625067981219
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 284, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 178, 1861, 18271, 183196, 1884205, 19328317, 201141637, 2097094975,
22004853520, 231614306320, 2446540491838, 25912508000887, 275122695839653
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 285, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 109, 811, 6391, 47521, 376489, 2937187, 23264659, 185072689, 1477981099,
11857932901, 95398253497, 769775390515, 6225910981309
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 286, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 23, 148, 1399, 12221, 111416, 1023968, 9495823, 88759435, 834019663,
7875349868, 74646026764, 709883092348, 6769870809872, 64719048195188
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 287, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 27, 187, 2035, 19371, 198861, 2021937, 20919123, 217314691, 2273060977,
23876367417, 251812893949, 2664297545365, 28269232393611, 300673258704027
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 288, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 31, 226, 2719, 27841, 310816, 3422476, 38393167, 432330643, 4901551111,
55810107706, 637990197076, 7316828619868, 84148498810624, 970111828316116
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 289, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 290, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 59, 352, 2212, 14639, 96826, 646048, 4350740, 29450728, 200260876,
1367195119, 9364357238, 64318682744, 442845544339
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 291, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 110, 736, 5952, 48444, 390504, 3222720, 26700320, 222282112, 1861053504,
15635874544, 131797101152, 1114112928192, 9440324644320
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 292, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 161, 1168, 11252, 102439, 939962, 8876032, 83484188, 792130696,
7553742572, 72246727711, 693579972854, 6676229315968, 64417508346041
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 293, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 50, 262, 1412, 7744, 43010, 241126, 1361660, 7733980, 44135060,
252851020, 1453385624, 8377694524, 48409438370
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 294, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 101, 742, 5692, 44279, 348973, 2776302, 22247120, 179305384, 1451969158,
11803779211, 96276318452, 787489979423, 6457021374286
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 295, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 152, 1270, 11532, 104364, 961116, 8930086, 83542796, 786199228,
7432817856, 70545012124, 671743016024, 6414432545616, 61400028720612
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 296, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 203, 1846, 18932, 188959, 1938239, 20009518, 207973544, 2175288472,
22850955074, 241001346139, 2550019889120, 27057140017951, 287788671418838
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 297, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 104, 712, 5072, 36544, 266912, 1967200, 14601920, 109006336, 817540352,
6155259136, 46494597632, 352187094016, 2674213712384
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 298, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 20, 155, 1336, 11692, 104399, 943630, 8610480, 79141844, 731648920,
6795953980, 63372712495, 592914790574, 5563039388612, 52323374287315
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 299, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 24, 206, 2008, 19872, 200124, 2042448, 21030496, 218145248, 2275699264,
23852014848, 250972308976, 2649449394464, 28048387826112, 297658339877856
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 300, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 28, 257, 2728, 29612, 324679, 3622166, 40695568, 460868828, 5247878968,
60040370876, 689576490079, 7945938584222, 91817719243852, 1063559968996217
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 301, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 170, 1366, 11732, 100504, 875954, 7700998, 68162012, 606845572,
5427408164, 48728213164, 438915525752, 3964510398892, 35895956728130
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 302, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 26, 221, 2134, 20932, 209039, 2115157, 21598462, 222173024, 2298591856,
23893662982, 249347367691, 2610737565620, 27412590681467, 288535722978646
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 303, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 30, 272, 2950, 31692, 349764, 3899100, 43901190, 497794700, 5677294180,
65052767760, 748317039100, 8636457510488, 99956164649280, 1159691439342132
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 304, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 34, 323, 3814, 44012, 523639, 6286583, 76238782, 931057496, 11436133984,
141127040738, 1748352464731, 21730705787936, 270856097780155,
3384226551825278
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 305, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 306, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 90, 645, 4653, 34504, 260319, 1982605, 15208911, 117362403, 909971604,
7083182544, 55317783186, 433240911879, 3401389973475
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 307, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 153, 1257, 10863, 97589, 884481, 8094529, 74684619, 693009657,
6460682121, 60467597529, 567798150663, 5346695047053, 50470035911073
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 308, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 216, 1917, 18873, 190944, 1940193, 19985373, 207391023, 2163802491,
22686481458, 238781051496, 2521447504254, 26700633678663, 283430285883171
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 309, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 87, 531, 3333, 21309, 138015, 902547, 5946153, 39406005, 262404585,
1754316045, 11767931451, 79165530375, 533883963567
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 310, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 150, 1239, 10563, 91804, 808272, 7184655, 64335993, 579488499,
5244519822, 47652399276, 434422880388, 3971722599360, 36401193762900
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 311, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 213, 1995, 19593, 195929, 1983999, 20284931, 208906809, 2163923253,
22520484759, 235295215989, 2466511223751, 25928668096431, 273236607114813
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 312, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 276, 2799, 30423, 334644, 3730716, 42007695, 476344257, 5432906187,
62255552076, 716166374724, 8265673738260, 95667463295088, 1109960564107476
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 313, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 159, 1233, 9843, 79989, 658143, 5465889, 45723363, 384694101, 3251864223,
27595902321, 234956883411, 2006117307957, 17170542663519
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 314, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 222, 2085, 20133, 198004, 1972575, 19840221, 201031647, 2048944815,
20983122240, 215740158720, 2225578627314, 23024747205807, 238791366352887
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 315, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 29, 285, 2985, 32223, 353969, 3938637, 44239169, 500533323, 5696099109,
65129071197, 747614001561, 8610311984823, 99446801724201, 1151402024923965
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 316, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 33, 348, 3933, 46113, 548844, 6621849, 80628333, 988897407, 12198777543,
151189535214, 1881150021144, 23483184599358, 293978478445167,
3689214649659183
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 317, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 243, 2187, 20493, 195129, 1880091, 18285507, 179113113, 1764495657,
17463682701, 173513183589, 1729616718339, 17289543598011, 173248733055843
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 318, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 31, 306, 3183, 34083, 371464, 4100988, 45707503, 513189945, 5795720631,
65766426498, 749233731156, 8564024112660, 98169292496544, 1128088286442756
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 319, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 35, 369, 4227, 49473, 590069, 7126395, 86884723, 1067042025, 13180777065,
163589364315, 2038335482445, 25482159109215, 319468518110595,
4014993050121249
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 320, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 39, 432, 5319, 66663, 851904, 11021832, 143944047, 1893563649, 25053740559,
333050216832, 4444732277676, 59513502554964, 799120028309040,
10756467370503972
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 321, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 322, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 3, 54, 90, 555, 1890, 6510, 34104, 89586, 568260, 1422531, 9081072,
24586848, 142705563
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 323, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 6, 216, 360, 4380, 15120, 97440, 544992, 2413152, 18073440, 67068144,
570810240, 2052198720, 17539538016
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 324, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 9, 486, 810, 14715, 51030, 481950, 2757888, 17176698, 136964520,
672962499, 6462480024, 28840975020, 295540974729
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 325, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 2, 9, 6, 60, 155, 315, 1582, 3780, 11592, 42570, 112299, 378378, 1219647,
3567564
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 326, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 12, 132, 440, 2870, 13020, 72100, 367248, 1945188, 10302600, 54299454,
290995848, 1542400574, 8295058772
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 327, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 15, 366, 1000, 12095, 50925, 454174, 2386860, 18396504, 108650850,
779959851, 4901037570, 34002807839, 220881360700
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 328, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 20, 18, 708, 1740, 31070, 125370, 1538404, 8172360, 82115460, 511269660,
4600061070, 31437204084, 265941660270, 1920529809198
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 329, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 36, 24, 480, 2320, 5040, 49504, 193536, 733824, 5005440, 19447296,
92911104, 519357696, 2165619456
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 330, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 39, 222, 1690, 8275, 62790, 355390, 2408952, 15154650, 97837740,
638712195, 4112747496, 26998857028, 175518862519
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 331, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 16, 42, 528, 3080, 23980, 182280, 1290688, 10362912, 74412576, 592653600,
4391928816, 34463677248, 261547329472, 2035429908512
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 332, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 22, 45, 942, 4650, 52675, 374850, 3427438, 28274400, 241966242, 2100819600,
17788547139, 156492198720, 1334189622480, 11749447034325
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 333, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 81, 54, 1620, 11475, 25515, 373086, 2020788, 8328096, 82996650, 419626251,
2347433946, 18626541219, 97173632556
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 334, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 84, 324, 4200, 21750, 185220, 1378020, 9654960, 77517972, 560138040,
4319736894, 32810561784, 248190577206, 1910801416524
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 335, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 87, 702, 6960, 45015, 465885, 3420942, 31646076, 260992368, 2266338690,
19641326859, 168546711762, 1476712358979, 12765083222892
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 336, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 24, 90, 1188, 9900, 84510, 878850, 7255332, 75547080, 661083444, 6606319500,
60934087566, 592462805220, 5628747475494, 54190076890950
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 337, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 338, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 22, 103, 451, 2056, 9787, 46327, 225967, 1101577, 5443912, 26988424,
134633968, 673909159, 3384842377
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 339, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 43, 313, 1621, 10081, 61363, 376993, 2407705, 15119413, 97922683,
627764809, 4091742877, 26590711993, 174165850963
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 340, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 64, 631, 3511, 27316, 188749, 1382599, 10333279, 75965149, 581289094,
4350397096, 33513132628, 254794267495, 1968761839609
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 341, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 3, 16, 55, 201, 816, 3228, 12783, 51523, 208483, 845868, 3448204, 14103532,
57829656, 237701376
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 342, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 37, 229, 1301, 7851, 47559, 291397, 1799317, 11167669, 69666609,
436177831, 2740122295, 17260940503, 108998027147
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 343, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 58, 511, 3121, 24096, 170220, 1283087, 9497587, 71685175, 540207570,
4100350420, 31177505308, 237913339392, 1819227859828
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 344, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 21, 79, 901, 5661, 52791, 405231, 3559893, 29451877, 255226561, 2174624211,
18844082071, 162696419731, 1414476472059, 12299835495969
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 345, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 49, 193, 1001, 6341, 33545, 185473, 1082065, 6119365, 34861025, 201562945,
1161389113, 6707737349, 38929010489
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 346, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 70, 439, 3291, 22676, 165551, 1202055, 8807551, 64986901, 481075376,
3577692856, 26685660496, 199616797615, 1496806789125
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 347, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 91, 793, 6301, 51461, 435107, 3632609, 31014217, 263924857, 2266951787,
19502967529, 168496623829, 1459244026397, 12669561636931
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 348, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 23, 112, 1255, 10031, 95936, 876233, 8230615, 77749807, 736364713,
7033571678, 67234817464, 646177199812, 6219097620815, 60048264570317
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 349, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 100, 415, 2761, 23716, 144712, 997711, 7478947, 51225967, 361809592,
2626630084, 18648796492, 133515159064, 965023408720
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 350, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 121, 733, 6781, 53671, 440203, 3731701, 31129573, 264009433, 2244464773,
19134087919, 163865679199, 1406297414731, 12100128720511
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 351, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 142, 1159, 11521, 99316, 955144, 8852719, 83961043, 798667459,
7620245854, 73134845356, 703218082828, 6785305011616, 65610936999172
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 352, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 163, 1693, 16981, 163891, 1723555, 17295685, 180988021, 1869009445,
19564502695, 204835762495, 2153989248139, 22710997599343, 239988664077733
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 353, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 354, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 47, 238, 1262, 6859, 38180, 216094, 1239860, 7190410, 42059360,
247728595, 1467332414, 8731277572, 52152609347
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 355, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 86, 568, 3752, 25564, 178712, 1265632, 9104288, 66121696, 484631072,
3576388336, 26546427104, 197976880768, 1482287736416
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 356, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 125, 1006, 7502, 59419, 478424, 3902350, 32394140, 270926962, 2290114004,
19475111539, 166678333382, 1433071275952, 12372546250745
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 357, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 29, 142, 672, 3219, 15717, 77550, 385040, 1921936, 9638202, 48521851,
245067032, 1241182011, 6301307934
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 358, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 68, 436, 2912, 19974, 139344, 982916, 6989720, 50010292, 359558784,
2595408094, 18796855508, 136519262598, 993947615048
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 359, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 107, 838, 6412, 51879, 424671, 3533758, 29660408, 250787968, 2131747026,
18198477499, 155900165072, 1339453334587, 11536897514542
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 360, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 24, 146, 1348, 11172, 102174, 928398, 8664996, 81347888, 771280564,
7350394548, 70400755726, 676718565824, 6525297383622, 63082176105906
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 361, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 68, 424, 2512, 16304, 107536, 703840, 4646336, 30942208, 206824576,
1386962944, 9333271040, 62983963904, 426023964928
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 362, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 107, 790, 6302, 50579, 411448, 3380654, 27966932, 232713394, 1945471288,
16327320211, 137477812214, 1160835229064, 9825733252727
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 363, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 20, 146, 1264, 11352, 103244, 958960, 8968320, 84596384, 802320160,
7645836640, 73144257520, 702033937568, 6756986492416, 65192852813856
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 364, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 26, 185, 1846, 17662, 177539, 1806772, 18583198, 192860636, 2012340826,
21106421932, 222208073971, 2347314722222, 24864956335028, 264035557782685
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 365, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 125, 862, 5912, 48619, 386885, 3008926, 24068960, 194053480, 1561400810,
12627434395, 102591165224, 835140360799, 6813604010870
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 366, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 164, 1300, 11792, 107974, 988472, 9194308, 86027960, 809204836,
7649884112, 72591979486, 691100890820, 6598091552446, 63145950761744
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 367, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 203, 1846, 18932, 188959, 1938239, 20009518, 207973544, 2175288472,
22850955074, 241001346139, 2550019889120, 27057140017951, 287788671418838
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 368, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 28, 242, 2500, 27332, 294814, 3292886, 36752356, 414831536, 4703094628,
53584658756, 612873962254, 7032350024624, 80919979013566, 933370060110362
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 369, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 370, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 84, 495, 3033, 19104, 122895, 803847, 5328669, 35709345, 241439850,
1644448320, 11268599904, 77609985111, 536792233659
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 371, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 141, 1017, 7623, 58569, 459693, 3666273, 29628123, 242007741, 1994256333,
16553858121, 138245736879, 1160397425313, 9781658699421
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 372, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 198, 1647, 14013, 122364, 1091961, 9891639, 90813069, 842480757,
7885027296, 74336316624, 705086271828, 6722010765063, 64361259732123
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 373, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 54, 303, 1743, 10064, 58488, 342799, 2024433, 12027051, 71788698,
430155636, 2585884356, 15588611112, 94201873344
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 374, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 111, 789, 5903, 45539, 358221, 2854693, 22958175, 185888637, 1513000371,
12366428919, 101425821669, 834286694783, 6879610345841
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 375, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 168, 1383, 11863, 105344, 955944, 8807983, 82033377, 770071743,
7272174264, 68995741164, 657063780948, 6276730763312, 60115676023108
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 376, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 29, 225, 2085, 19623, 192719, 1931037, 19681909, 202928463, 2110665609,
22097546397, 232534965111, 2456944843473, 26045817852531, 276868300728015
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 377, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 99, 753, 5403, 39229, 291819, 2195041, 16597683, 126137133, 963202419,
7384086609, 56789615691, 437959781853, 3385645890939
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 378, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 156, 1311, 11473, 102604, 929547, 8503063, 78356685, 726274989,
6763643802, 63236216976, 593184569760, 5580127723231, 52621419169831
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 379, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 213, 1977, 19343, 193549, 1969845, 20263777, 210108939, 2191759425,
22973774805, 241762494345, 2552615050599, 27027715134949, 286875624839333
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 380, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 31, 270, 2751, 29013, 315304, 3492093, 39137863, 442540989, 5036148801,
57602792448, 661537608576, 7623091184868, 88094071532463, 1020533368904415
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 381, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 162, 1431, 11583, 99684, 886140, 7864047, 70025553, 628467255,
5669425710, 51312837420, 465873751476, 4241819032200, 38714898642192
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 382, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 219, 2061, 20103, 201759, 2043513, 20886357, 215095503, 2227784481,
23181720543, 242168099391, 2538160889085, 26677526149491, 281081075987229
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 383, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 276, 2799, 30423, 334644, 3730716, 42007695, 476344257, 5432906187,
62255552076, 716166374724, 8265673738260, 95667463295088, 1109960564107476
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 384, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 33, 333, 3645, 42543, 501579, 6027129, 73070181, 892691199, 10969766253,
135434923209, 1678652780319, 20874498339321, 260310127316391,
3254026087212363
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 385, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 386, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 12, 54, 360, 780, 7560, 19110, 141456, 514836, 2688840, 12775356,
55783728, 293775768, 1254965712
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 387, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 24, 216, 1440, 5280, 60480, 198240, 2220288, 9217152, 78946560,
428338944, 2905943040, 18839208960, 113845315584
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 388, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 36, 486, 3240, 16740, 204120, 822150, 11167632, 51621948, 581537880,
3411250524, 30578564016, 218380785480, 1679415834096
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 389, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 9, 24, 120, 295, 1260, 4144, 14364, 53424, 182160, 669471, 2378376,
8547396, 30999969
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 390, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 21, 222, 910, 6475, 33810, 214270, 1226568, 7519050, 44643060, 271738995,
1639421784, 9987222388, 60747067381
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 391, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 16, 33, 528, 2420, 22855, 143220, 1139488, 8072988, 60993576, 452043900,
3381052191, 25456211352, 190893946672, 1445604273113
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 392, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 22, 45, 942, 4650, 52675, 374850, 3427438, 28274400, 241966242, 2100819600,
17788547139, 156492198720, 1334189622480, 11749447034325
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 393, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 36, 96, 960, 3440, 20160, 114688, 532224, 3161088, 16220160, 87039744,
482347008, 2547038208, 14031553536
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 394, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 48, 438, 2720, 19340, 137760, 964390, 7017024, 50038884, 364980000,
2642109756, 19317355200, 141107646680, 1035194608448
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 395, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 20, 60, 888, 5200, 51920, 386400, 3447136, 28049280, 242645760, 2043888000,
17583244800, 150328189440, 1295381914112, 11159026278400
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 396, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 26, 72, 1446, 8400, 104420, 811440, 8573446, 75364128, 751104396, 6967485360,
68083216476, 647328341088, 6292354400904, 60564396084192
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 397, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 81, 216, 3240, 15255, 102060, 825552, 4592700, 35026992, 236720880,
1553288319, 11281193352, 75436882092, 525411447561
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 398, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 93, 702, 6510, 45195, 410130, 3196830, 27180552, 225560538, 1888355700,
15956447859, 134330645592, 1140101509404, 9668650244253
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 399, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 24, 105, 1296, 10500, 98295, 926100, 8481984, 81711420, 763585704,
7355432700, 69944084991, 674045812440, 6476674525464, 62569963481025
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 400, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 30, 117, 1998, 15210, 177795, 1695330, 18054414, 185159520, 1940517810,
20368473840, 214148236995, 2267127061056, 23981812466040, 255038251745277
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 401, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 402, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 31, 139, 811, 4081, 23017, 126211, 704515, 3964117, 22326877, 126623509,
719388853, 4101044143, 23432673271
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 403, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 61, 385, 2881, 17821, 136333, 927361, 6836353, 49118893, 358299613,
2624654209, 19225786945, 141731035837, 1044701312941
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 404, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 91, 739, 6211, 44461, 407989, 3141811, 27794611, 229228489, 1976011489,
16840543501, 144475141357, 1245842151139, 10729407983131
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 405, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 22, 85, 371, 1616, 7085, 31501, 140845, 633235, 2860760, 12972400,
59015698, 269229455, 1231171037
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 406, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 52, 367, 2331, 15836, 106961, 734007, 5060815, 35122741, 244814846,
1713217936, 12027863056, 84680593687, 597624238677
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 407, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 82, 757, 5551, 46196, 373997, 3099965, 25778917, 215711767, 1814123312,
15307993504, 129640671694, 1100704760039, 9369279969157
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 408, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 23, 112, 1255, 10031, 95936, 876233, 8230615, 77749807, 736364713,
7033571678, 67234817464, 646177199812, 6219097620815, 60048264570317
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 409, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 61, 289, 1881, 11481, 69189, 435009, 2715505, 17052649, 107911629,
684134881, 4353063625, 27780372153, 177671688021
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 410, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 91, 715, 5531, 43401, 347565, 2794051, 22682899, 184983085, 1516274145,
12474913045, 102976097173, 852405168343, 7073074138691
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 411, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 21, 121, 1249, 10441, 97941, 892641, 8349377, 78118033, 737035861,
6978684681, 66360270241, 632981525593, 6054915252309, 58058495769841
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 412, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 27, 151, 1891, 16611, 178341, 1772457, 18565107, 191755843, 2012282017,
21109667877, 222836425549, 2357192730205, 25018285817643, 266101374484791
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 413, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 118, 613, 5251, 39736, 287533, 2270605, 17420941, 134426683, 1053142168,
8222381344, 64507816738, 508027777375, 4005588284893
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 414, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 148, 1183, 11131, 96916, 891409, 8162743, 75430255, 701729869,
6551407534, 61437972256, 577905187120, 5451487479751, 51549534477733
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 415, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 178, 1861, 18271, 183196, 1884205, 19328317, 201141637, 2097094975,
22004853520, 231614306320, 2446540491838, 25912508000887, 275122695839653
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 416, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 31, 208, 2647, 26671, 301816, 3333961, 37594327, 425795023, 4849606081,
55526229166, 637836174856, 7353643604932, 84996955243903, 984936321078013
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 417, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 418, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 56, 310, 1892, 11764, 74720, 481702, 3134396, 20545420, 135412400,
896364220, 5954542856, 39672766696, 264987737216
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 419, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 104, 712, 5552, 42304, 337472, 2709088, 22004672, 180130816, 1482313472,
12256066816, 101691700736, 846323488768, 7061334370304
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 420, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 152, 1222, 11012, 94924, 879104, 8055814, 75377276, 708583732,
6702934064, 63721287964, 607792062152, 5816336101528, 55797203442752
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 421, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 41, 208, 1072, 5639, 30046, 161536, 874652, 4763008, 26058496, 143119519,
788623214, 4357696568, 24137804161
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 422, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 89, 646, 4802, 36539, 281668, 2192558, 17192420, 135593314, 1074441568,
8547195331, 68217505670, 545999650616, 4380746574869
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 423, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 20, 137, 1192, 10332, 92759, 843670, 7754352, 71825276, 669148600,
6263877820, 58863975295, 554990112926, 5247322710244, 49732947077217
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 424, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 26, 185, 1846, 17662, 177539, 1806772, 18583198, 192860636, 2012340826,
21106421932, 222208073971, 2347314722222, 24864956335028, 264035557782685
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 425, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 92, 592, 4032, 28464, 201504, 1439232, 10364672, 75039232, 545731584,
3984342784, 29183499776, 214347856896, 1578137951232
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 426, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 140, 1174, 10172, 89364, 796056, 7155110, 64782572, 589921948,
5397220776, 49572508924, 456817283288, 4221516171240, 39106924773680
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 427, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 24, 188, 1864, 18112, 182064, 1845888, 18912352, 195108416, 2024531584,
21105295488, 220874146816, 2319108947456, 24418300664320, 257729407433728
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 428, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 30, 236, 2662, 27852, 309804, 3441720, 38810118, 439975820, 5020019140,
57530213160, 661921766620, 7640502079160, 88441612221720, 1026220606945776
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 1, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 429, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 161, 1168, 9632, 82999, 701822, 6027424, 52294652, 455128576, 3980529632,
34957736191, 307936960814, 2720091434272, 24085600569881
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 430, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 209, 1894, 18722, 184699, 1850564, 18722638, 190691300, 1953749362,
20110451264, 207809229379, 2154452620166, 22399057482208, 233442446848109
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 431, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 28, 257, 2728, 29612, 324679, 3622166, 40695568, 460868828, 5247878968,
60040370876, 689576490079, 7945938584222, 91817719243852, 1063559968996217
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 432, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 34, 305, 3670, 42302, 506179, 6107348, 74408254, 913231772, 11270061034,
139746563948, 1739450879731, 21722649705902, 272034802759516,
3414991429703285
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 433, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 434, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 93, 603, 4113, 29049, 209835, 1539939, 11430345, 85551885, 644363415,
4877033445, 37057558671, 282479087367, 2159021017653
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 435, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 159, 1233, 10323, 88629, 779103, 6960417, 62887587, 573028821,
5254737183, 48425629041, 448037751411, 4158668284533, 38704583832159
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 436, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 225, 1971, 18873, 182709, 1823391, 18457875, 189056025, 1953345537,
20311790931, 212286973149, 2227601718423, 23451644875707, 247566248826705
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 437, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 72, 429, 2613, 16144, 100929, 636925, 4048839, 25887483, 166302414,
1072532184, 6940009170, 45033929079, 292943440647
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 438, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 138, 1095, 9073, 77044, 664317, 5788519, 50829213, 449013069, 3985601832,
35518288056, 317584289376, 2847755324839, 25598520695623
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 439, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 204, 1869, 17873, 175684, 1756905, 17771245, 181242591, 1859938335,
19180826910, 198596982120, 2063136787182, 21493951800031, 224474815572719
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 440, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 31, 270, 2751, 29013, 315304, 3492093, 39137863, 442540989, 5036148801,
57602792448, 661537608576, 7623091184868, 88094071532463, 1020533368904415
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 441, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 135, 1041, 8043, 63569, 509631, 4120993, 33553683, 274761297, 2260414071,
18667758129, 154671536763, 1285110440337, 10703354414895
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 442, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 201, 1851, 17633, 171089, 1681599, 16685923, 166785177, 1676848293,
16939092459, 171789670149, 1748022315471, 17837360202671, 182465597624561
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 443, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 29, 267, 2769, 29563, 322829, 3573027, 39933217, 449598579, 5091390909,
57928915707, 661687723761, 7583049315819, 87148577826605, 1004007555520147
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 444, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 35, 333, 3795, 43833, 522029, 6297315, 76778515, 943058025, 11651905305,
144645447015, 1802646808125, 22539573912807, 282619738055235,
3552351378345693
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 445, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 216, 1917, 17253, 161784, 1531953, 14596605, 140153895, 1353650211,
13132484478, 127891753416, 1249543617858, 12242332028871, 120231780433191
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 446, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 282, 2871, 30513, 329964, 3610701, 39892071, 443946045, 4969177317,
55884278376, 630954015624, 7147318455072, 81192874716183, 924604690710327
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 447, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 33, 348, 3933, 46113, 548844, 6621849, 80628333, 988897407, 12198777543,
151189535214, 1881150021144, 23483184599358, 293978478445167,
3689214649659183
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 448, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 39, 414, 5103, 64053, 821664, 10678797, 140083911, 1851108957, 24601398489,
328492431072, 4403316869136, 59219110694916, 798665316014367,
10797531402095919
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 449, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 3/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 450, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 46, 199, 1411, 8056, 49267, 309751, 1901935, 11977417, 75228352,
474478984, 3007561168, 19088361943, 121528903321
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 451, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 91, 505, 4981, 33121, 278083, 2180641, 17214553, 140291893, 1120096363,
9118057609, 73972081405, 602505781177, 4924434083491
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 452, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 136, 919, 10711, 78436, 811189, 7132231, 66785311, 631180189, 5847324814,
55736022376, 524057651092, 4984321672279, 47380317974281
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 453, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 3/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 28, 127, 601, 2836, 13672, 66319, 324163, 1593487, 7868752, 39007684,
193998988, 967517656, 4836876688
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 454, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 73, 541, 3901, 28711, 215083, 1618933, 12302821, 93920473, 720669973,
5550284719, 42888269503, 332329270027, 2581379971183
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 455, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 118, 1063, 9361, 81316, 743464, 6674095, 61288435, 561646819, 5188163014,
48049343596, 446613538060, 4162613091040, 38889202725028
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 456, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 163, 1693, 16981, 163891, 1723555, 17295685, 180988021, 1869009445,
19564502695, 204835762495, 2153989248139, 22710997599343, 239988664077733
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 457, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 3/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 73, 433, 3001, 19261, 130033, 878305, 5963761, 40837933, 280474393,
1934740369, 13388260393, 92896734685, 646162569793
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 458, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 118, 1063, 8731, 75916, 659359, 5805703, 51411295, 458084269, 4100076784,
36841864456, 332129714320, 3002567395231, 27210163458133
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 459, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 163, 1801, 16621, 169021, 1685755, 17174977, 175424617, 1805017825,
18647693395, 193433769145, 2012924810053, 21005971610677, 219738531772603
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 460, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 31, 208, 2647, 26671, 301816, 3333961, 37594327, 425795023, 4849606081,
55526229166, 637836174856, 7353643604932, 84996955243903, 984936321078013
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 461, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 3/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 136, 919, 8281, 63856, 530524, 4424239, 36718435, 309538099, 2609332804,
22100968396, 187876087660, 1600637137048, 13673650194496
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 462, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 181, 1765, 16981, 164251, 1631575, 16219141, 163031509, 1645522885,
16695438145, 170022115495, 1737195291703, 17799551994823, 182818704607291
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 463, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 31, 226, 2719, 27841, 310816, 3422476, 38393167, 432330643, 4901551111,
55810107706, 637990197076, 7316828619868, 84148498810624, 970111828316116
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 464, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 37, 271, 3781, 40861, 506791, 6027967, 74098837, 907716133, 11235051217,
139416470227, 1738293567319, 21735574815475, 272588760670123,
3426566851657441
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 1
The congruence classes mod, 2, in the following set , {0}, never show up!
Theorem Number, 465, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 3/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 466, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 71, 430, 2942, 20539, 144020, 1025182, 7346996, 52942570, 383400800,
2787170995, 20328011966, 148678494436, 1090065392891
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 467, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 134, 952, 8552, 72604, 635672, 5652448, 50332832, 452264416, 4079466272,
36940159216, 335653543136, 3058081779328, 27930195838304
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 468, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 197, 1582, 16862, 159499, 1622504, 16490254, 168244316, 1736707282,
17949522164, 186508941139, 1943706569222, 20311508666128, 212793921527777
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 469, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 3/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 53, 286, 1592, 9019, 51725, 299422, 1745792, 10237480, 60315290,
356740795, 2116928504, 12597419215, 75147483158
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 470, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 116, 916, 7472, 61894, 519752, 4404292, 37594232, 322745956, 2783809712,
24105317086, 209419347620, 1824503882686, 15934258258496
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 471, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 179, 1654, 16052, 156079, 1550999, 15504430, 156274568, 1583754712,
16125974834, 164835049339, 1690401666800, 17383950058063, 179208657048374
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 472, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 28, 242, 2500, 27332, 294814, 3292886, 36752356, 414831536, 4703094628,
53584658756, 612873962254, 7032350024624, 80919979013566, 933370060110362
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 473, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 3/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 116, 808, 6032, 45424, 345872, 2660704, 20606912, 160504576, 1255970432,
9865916416, 77751386624, 614452786432, 4867614976256
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 474, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 179, 1654, 15422, 146899, 1415864, 13776718, 135021140, 1330957762,
13181632664, 131060482579, 1307396822006, 13078832786608, 131156898478559
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 475, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 28, 242, 2608, 27512, 299404, 3287216, 36460288, 407220128, 4574510368,
51627802976, 584937681904, 6649057311392, 75793079942272, 866072413378592
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 476, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 34, 305, 3670, 42302, 506179, 6107348, 74408254, 913231772, 11270061034,
139746563948, 1739450879731, 21722649705902, 272034802759516,
3414991429703285
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 477, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 3/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 197, 1582, 14432, 130339, 1188749, 10992622, 102170672, 955182832,
8972492234, 84596753179, 800223519656, 7590561630331, 72173424715982
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 478, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 28, 260, 2644, 27872, 296614, 3206576, 34956100, 383915672, 4240653748,
47061843776, 524325629854, 5860892884628, 65697830284870, 738240048624680
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 479, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 34, 323, 3814, 44012, 523639, 6286583, 76238782, 931057496, 11436133984,
141127040738, 1748352464731, 21730705787936, 270856097780155,
3384226551825278
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
Theorem Number, 480, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 40, 386, 5092, 62852, 814654, 10576190, 139081828, 1839831920, 24487567540,
327396267860, 4394457784270, 59176751771360, 799127466216070,
10817660930841026
We are interested in A(n) modulo , 2
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 2, equals , 0
all the congruences classes mod, 2, show up
This ends this fascinating book that took, 2.472, to generate.
----------------------------------------------------------
--------------------------------------
On computing the Mod, 4, of Many Interesting sequences
by Shalosh B. Ekhad
Theorem Number, 1, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 14, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 2, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 23, 94, 402, 1779, 8052, 37006, 171932, 805186, 3793572, 17957251,
85323734, 406676976, 1943412483
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 50, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 3, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 38, 184, 952, 5084, 27736, 153696, 860960, 4861408, 27616096, 157617904,
903002336, 5189453312, 29901183328
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 15, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 4, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 53, 286, 1682, 10099, 62120, 388126, 2451140, 15606970, 99979640,
643535875, 4158061598, 26950603060, 175140491273
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 5, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 23, 94, 392, 1659, 7107, 30734, 133880, 586576, 2582142, 11411371,
50597900, 224986467, 1002867878
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 6, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 38, 196, 1052, 5774, 32146, 180772, 1024256, 5837908, 33433996, 192239854,
1109049320, 6416509142, 37215072638
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 14, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 7, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 53, 310, 1892, 11839, 75245, 483326, 3128768, 20375440, 133329110,
875909995, 5773461956, 38163131387, 252880464038
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 8, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 68, 436, 2912, 19974, 139344, 982916, 6989720, 50010292, 359558784,
2595408094, 18796855508, 136519262598, 993947615048
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 18, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 9, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 44, 232, 1232, 6704, 36976, 205664, 1151936, 6489088, 36724096, 208635904,
1189162496, 6796807424, 38941961984
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 14, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 10, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 59, 358, 2242, 14299, 92360, 602270, 3956252, 26140330, 173541260,
1156667395, 7734994958, 51873729652, 348741401119
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 11, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 74, 496, 3432, 24204, 172944, 1247488, 9064352, 66245152, 486431904,
3585858544, 26521709216, 196715685248, 1462647306144
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 15, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 12, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 89, 646, 4802, 36539, 281668, 2192558, 17192420, 135593314, 1074441568,
8547195331, 68217505670, 545999650616, 4380746574869
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 13, : Let A(n) be the constant term, in x, of
/ 1 \n
|2 + ---- + 1/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 71, 430, 2672, 17299, 112835, 740926, 4904360, 32649640, 218325230,
1465532875, 9869605436, 66650927815, 451185626366
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 14, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 86, 580, 4092, 29454, 214314, 1574500, 11652224, 86731012, 648619644,
4869770734, 36682896824, 277107171150, 2098432827606
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 14, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 15, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 101, 742, 5692, 44279, 348973, 2776302, 22247120, 179305384, 1451969158,
11803779211, 96276318452, 787489979423, 6457021374286
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 16, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 116, 916, 7472, 61894, 519752, 4404292, 37594232, 322745956, 2783809712,
24105317086, 209419347620, 1824503882686, 15934258258496
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 18, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 17, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 22, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 18, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 48, 231, 1173, 6164, 33183, 181799, 1008957, 5653701, 31912818,
181156776, 1032969564, 5911392015, 33930026163
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 35, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 19, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 69, 393, 2343, 14449, 91269, 586497, 3816411, 25066773, 165813189,
1102873209, 7367533839, 49390996521, 332074347189
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 20, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 90, 567, 3753, 25704, 180225, 1285335, 9281709, 67649985, 496555920,
3664741320, 27164429568, 202060317663, 1507366068435
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 21, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 48, 231, 1163, 5984, 31188, 164047, 869097, 4631211, 24797028, 133302156,
719013636, 3889437080, 21091925888
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 22, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 69, 405, 2503, 15919, 103029, 674613, 4454223, 29596473, 197645649,
1325302119, 8917233705, 60174146899, 407079536539
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 22, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 23, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 90, 591, 4083, 29064, 210780, 1547695, 11464281, 85477095, 640576170,
4820411220, 36398556756, 275640152992, 2092580941860
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 24, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 111, 789, 5903, 45539, 358221, 2854693, 22958175, 185888637, 1513000371,
12366428919, 101425821669, 834286694783, 6879610345841
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 30, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 25, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 75, 465, 2923, 18589, 119619, 777121, 5085651, 33473133, 221347899,
1469414769, 9786831291, 65367631741, 437665012915
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 22, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 26, : Let A(n) be the constant term, in x, of
/ 1 2\n
|3 + ---- + 1/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 96, 663, 4733, 34464, 254355, 1895735, 14235693, 107538705, 816302490,
6221251320, 47574051372, 364849702967, 2805038513231
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 34, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 27, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 117, 873, 6783, 53909, 434661, 3540161, 29052459, 239840217, 1989519381,
16569202329, 138455300727, 1160272014989, 9747281151477
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 28, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 138, 1095, 9073, 77044, 664317, 5788519, 50829213, 449013069, 3985601832,
35518288056, 317584289376, 2847755324839, 25598520695623
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 29, : Let A(n) be the constant term, in x, of
/ 1 \n
|3 + ---- + 1/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 108, 783, 5643, 41364, 307800, 2311983, 17485065, 132980535, 1016080200,
7793724420, 59975964324, 462830103576, 3580271880048
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 11, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 30, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 129, 1005, 7983, 64619, 530001, 4388645, 36608511, 307172637, 2589753741,
21920819919, 186169052241, 1585620914055, 13538300225319
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 22, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 31, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 150, 1239, 10563, 91804, 808272, 7184655, 64335993, 579488499,
5244519822, 47652399276, 434422880388, 3971722599360, 36401193762900
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 32, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 171, 1485, 13383, 123039, 1146393, 10784853, 102210255, 974339361,
9332293743, 89738353791, 865787580765, 8376809358771, 81248052512781
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 30, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 33, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2, 3}, never show up!
Theorem Number, 34, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 2, 12, 6, 120, 260, 840, 4550, 10416, 50652, 175560, 571164, 2450448,
7979400, 30702672
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 35, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 24, 24, 480, 1120, 6720, 36960, 123648, 814464, 3252480, 16279296,
83026944, 363297792, 1912694784
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2, 3}, never show up!
Theorem Number, 36, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 36, 54, 1080, 2700, 22680, 126630, 553392, 4143636, 18711000, 118713276,
665512848, 3580258968, 21938572656
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 37, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 3, 24, 40, 175, 420, 1456, 4116, 13104, 39600, 122991, 380952, 1180036,
3686683
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 38, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 15, 78, 350, 1515, 7350, 32942, 157920, 734706, 3498000, 16578771,
79073280, 377947856, 1810383575
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 39, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 27, 144, 900, 4175, 26460, 136640, 805140, 4489128, 25678620, 147274479,
842037768, 4863568424, 27995674707
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 40, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 39, 222, 1690, 8275, 62790, 355390, 2408952, 15154650, 97837740,
638712195, 4112747496, 26998857028, 175518862519
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 41, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 12, 96, 320, 1520, 6720, 28672, 134400, 580608, 2703360, 12021504,
55351296, 250984448, 1151101952
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2, 3}, never show up!
Theorem Number, 42, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 24, 198, 880, 5380, 28560, 164934, 924000, 5303340, 30299280, 174574620,
1006825248, 5829520840, 33815445664
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 43, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 36, 312, 1680, 11280, 70560, 458080, 2975616, 19418112, 127670400,
840390144, 5560828416, 36850418176, 244984836096
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2, 3}, never show up!
Theorem Number, 44, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 48, 438, 2720, 19340, 137760, 964390, 7017024, 50038884, 364980000,
2642109756, 19317355200, 141107646680, 1035194608448
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 45, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 27, 216, 1080, 5535, 34020, 172368, 1041012, 5633712, 32717520,
184926159, 1058315544, 6083437932, 34854046227
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 46, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 39, 366, 1950, 13355, 84630, 555086, 3660384, 24151554, 160995120,
1072726611, 7191385344, 48262029816, 324988783119
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 47, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 16, 51, 528, 3060, 23935, 164220, 1219680, 8809332, 65106216, 479262300,
3556725711, 26425456200, 197088262800, 1472727467211
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 15, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 48, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 63, 702, 4410, 37395, 277830, 2235870, 17495352, 140056938, 1117046700,
8979363459, 72278197992, 583933176684, 4727043624303
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 49, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 50, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 3, 19, 67, 291, 1341, 5853, 26419, 120403, 547993, 2513193, 11570989,
53408941, 247299027, 1147809939
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 51, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 37, 145, 881, 4901, 26405, 152097, 857953, 4884805, 28079525, 161316145,
931359313, 5392226789, 31279571237
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 52, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 55, 235, 1771, 10801, 67537, 450115, 2882467, 18952597, 124876357,
822501109, 5456962837, 36235266991, 241267084975
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 53, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 16, 61, 231, 896, 3515, 13917, 55501, 222595, 896930, 3628120, 14724022,
59922175, 244456581
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 35, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 54, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 34, 175, 951, 5176, 28687, 160231, 901663, 5103097, 29016472, 165634624,
948599692, 5447994839, 31365144909
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 55, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 52, 301, 1971, 12396, 80739, 527437, 3472261, 23001919, 153016194,
1022072536, 6848799010, 46022234519, 310008304797
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 56, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 70, 439, 3291, 22676, 165551, 1202055, 8807551, 64986901, 481075376,
3577692856, 26685660496, 199616797615, 1496806789125
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 57, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 37, 193, 1001, 5241, 28029, 150529, 815761, 4443049, 24314709, 133573441,
736168057, 4068611353, 22540316717
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 58, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 55, 355, 2211, 14261, 92681, 608819, 4026691, 26789041, 179056901,
1201500301, 8088847261, 54610234459, 369590414295
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 59, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 73, 529, 3721, 26941, 197233, 1456673, 10840465, 81117613, 609893593,
4603215409, 34857719833, 264699597917, 2014944995713
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 60, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 91, 715, 5531, 43401, 347565, 2794051, 22682899, 184983085, 1516274145,
12474913045, 102976097173, 852405168343, 7073074138691
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 61, : Let A(n) be the constant term, in x, of
/ 1 \n
|1 + ---- + 2/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 64, 397, 2551, 15976, 104203, 676957, 4447981, 29366443, 194743858,
1296733384, 8661154438, 58014153679, 389517227749
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 35, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 62, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 82, 607, 4311, 31536, 233535, 1743463, 13120255, 99267985, 754699320,
5759824720, 44104291180, 338667328455, 2606900765757
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 63, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 100, 829, 6371, 51476, 416627, 3415245, 28165861, 233706727, 1948038962,
16301553544, 136861333714, 1152270624935, 9724867347485
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 64, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 118, 1063, 8731, 75916, 659359, 5805703, 51411295, 458084269, 4100076784,
36841864456, 332129714320, 3002567395231, 27210163458133
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 65, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 66, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 32, 166, 852, 4524, 24432, 132934, 728348, 4014676, 22233312, 123605596,
689449256, 3856481880, 21624138912
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 67, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 56, 328, 2032, 13184, 85696, 562272, 3721664, 24763648, 165534976,
1110924544, 7479881216, 50503294976, 341822273536
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 68, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 80, 502, 3572, 26164, 190640, 1411750, 10529756, 78907660, 594342080,
4493839420, 34087429352, 259297309288, 1977203630240
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 69, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 35, 160, 752, 3599, 17446, 85376, 420884, 2087008, 10398016, 52010479,
261021854, 1313707256, 6628095035
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 70, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 59, 358, 2242, 14299, 92360, 602270, 3956252, 26140330, 173541260,
1156667395, 7734994958, 51873729652, 348741401119
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 71, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 83, 568, 4092, 29919, 221454, 1655056, 12458036, 94317592, 717428604,
5478493519, 41973619118, 322490785244, 2483811265323
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 72, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 107, 790, 6302, 50579, 411448, 3380654, 27966932, 232713394, 1945471288,
16327320211, 137477812214, 1160835229064, 9825733252727
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 73, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 68, 400, 2432, 15024, 93984, 593408, 3773696, 24136192, 155096064,
1000509184, 6475410944, 42027531264, 273436525568
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 74, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 92, 646, 4652, 34124, 253528, 1901638, 14368844, 109208164, 833981128,
6394017436, 49185717752, 379438594136, 2934361958192
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 75, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 116, 904, 7232, 58864, 485312, 4038752, 33856064, 285456256, 2418204032,
20565984256, 175486400000, 1501643090432, 12881109687296
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 76, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 140, 1174, 10172, 89364, 796056, 7155110, 64782572, 589921948,
5397220776, 49572508924, 456817283288, 4221516171240, 39106924773680
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 77, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 107, 736, 5312, 38719, 286022, 2132512, 16011188, 120903136, 917200352,
6985016911, 53368875614, 408904516960, 3140554335587
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 78, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 131, 1030, 8322, 68379, 569256, 4783678, 40494812, 344797498, 2949775116,
25335206659, 218324891150, 1886757094044, 16345408354311
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 79, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 20, 155, 1336, 11692, 104399, 943630, 8610480, 79141844, 731648920,
6795953980, 63372712495, 592914790574, 5563039388612, 52323374287315
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 80, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 179, 1654, 15422, 146899, 1415864, 13776718, 135021140, 1330957762,
13181632664, 131060482579, 1307396822006, 13078832786608, 131156898478559
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 81, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 82, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 57, 339, 2073, 12869, 81063, 516371, 3315513, 21415761, 138994683,
905707581, 5921485911, 38825170731, 255192103017
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 83, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 87, 609, 4323, 31549, 234279, 1757121, 13276995, 100922733, 770828919,
5910673569, 45473210019, 350836300317, 2713419535047
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 84, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 117, 891, 6993, 56889, 469395, 3909411, 32816745, 277120845, 2351230335,
20027470725, 171156328047, 1466848379655, 12601932138477
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 85, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 66, 357, 1993, 11344, 65439, 381229, 2237799, 13214763, 78417144,
467210544, 2793104694, 16746295159, 100655033791
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 36, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 86, : Let A(n) be the constant term, in x, of
/ 1 2\n
|3 + ---- + 2/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 96, 663, 4733, 34464, 254355, 1895735, 14235693, 107538705, 816302490,
6221251320, 47574051372, 364849702967, 2805038513231
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 34, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 87, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 126, 981, 7893, 64844, 539871, 4538333, 38433663, 327393927, 2802193056,
24079196304, 207602903394, 1794990074783, 15558234035031
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 88, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 156, 1311, 11473, 102604, 929547, 8503063, 78356685, 726274989,
6763643802, 63236216976, 593184569760, 5580127723231, 52621419169831
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 35, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 89, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 111, 753, 5243, 37169, 266871, 1934305, 14122803, 103715217, 765283071,
5669058129, 42134877099, 314054824625, 2346580226951
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 90, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 141, 1107, 8953, 73789, 616227, 5196627, 44152809, 377379369, 3241135527,
27948336381, 241813226151, 2098240353907, 18252025766941
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 6, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 91, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 171, 1473, 13083, 118389, 1085283, 10044673, 93656115, 878386581,
8277708123, 78317021121, 743453353035, 7077691236469, 67546304093331
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 92, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 201, 1851, 17633, 171089, 1681599, 16685923, 166785177, 1676848293,
16939092459, 171789670149, 1748022315471, 17837360202671, 182465597624561
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 93, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 162, 1269, 10233, 84024, 698463, 5860269, 49524615, 420938451,
3594605688, 30815984736, 265051212390, 2286157926087, 19766997379647
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 36, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 94, : Let A(n) be the constant term, in x, of
/ 1 2\n
|3 + ---- + 2/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 192, 1671, 14973, 136664, 1263699, 11798327, 110974989, 1050011433,
9982721994, 95287086024, 912593172780, 8765282582247, 84397758645087
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 34, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 95, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 222, 2085, 20133, 198004, 1972575, 19840221, 201031647, 2048944815,
20983122240, 215740158720, 2225578627314, 23024747205807, 238791366352887
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 96, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 252, 2511, 25713, 268164, 2832651, 30206871, 324489645, 3506130117,
38064293226, 414877585824, 4536977899392, 49756312005903, 547012699861527
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 35, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 97, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 9, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2, 3}, never show up!
Theorem Number, 98, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 2, 27, 6, 270, 1235, 1890, 22750, 72576, 255402, 1746360, 5493939, 26594568,
135246540, 485431947
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 99, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 54, 24, 1080, 5020, 15120, 182560, 671328, 4090464, 28939680, 123872496,
861404544, 4873083072, 25497055584
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 100, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 81, 54, 2430, 11475, 51030, 618030, 2571912, 20728386, 151559100,
809349651, 6620101488, 41146707888, 270064675881
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 50, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 101, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 3, 54, 60, 555, 945, 6174, 13692, 72576, 191070, 887931, 2617758,
11184459, 35543508
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 102, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 30, 132, 900, 3950, 24150, 126308, 701400, 3925908, 21624900, 121975854,
681415020, 3840592470, 21661690050
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 14, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 103, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 57, 222, 2280, 10975, 81795, 530670, 3381924, 23536800, 152618070,
1039404795, 6982162902, 47006723907, 319562335092
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 32, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 104, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 84, 324, 4200, 21750, 185220, 1378020, 9654960, 77517972, 560138040,
4319736894, 32810561784, 248190577206, 1910801416524
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 17, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 105, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 12, 216, 480, 4560, 15120, 106848, 440832, 2685312, 12481920, 70608384,
349899264, 1910168832, 9793335552
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 9, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2, 3}, never show up!
Theorem Number, 106, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 39, 366, 1950, 13355, 84630, 555086, 3660384, 24151554, 160995120,
1072726611, 7191385344, 48262029816, 324988783119
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 107, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 16, 66, 528, 3960, 26860, 212520, 1525440, 11760672, 88202016, 674018400,
5147940336, 39453860160, 303552300480, 2338399199136
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 108, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 93, 702, 6510, 45195, 410130, 3196830, 27180552, 225560538, 1888355700,
15956447859, 134330645592, 1140101509404, 9668650244253
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 109, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 27, 486, 1620, 15795, 76545, 581742, 3367980, 23147208, 145063710,
961967259, 6231677166, 40944989943, 268823406852
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 110, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 20, 54, 708, 3780, 33230, 224910, 1780324, 13086360, 101075940, 765885780,
5900921070, 45300140028, 350025900510, 2705769780714
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 14, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 111, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 22, 81, 942, 6480, 56455, 456435, 3829630, 32176116, 271455912, 2307734550,
19643430939, 168054990246, 1440139057071, 12379261890996
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 32, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 112, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 24, 108, 1188, 9720, 85590, 782460, 6928740, 63930384, 579843684, 5355088200,
49289858046, 456764485320, 4238037731070, 39439963911348
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 17, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 113, : Let A(n) be the constant term, in x, of
/ 1 \n
|1 + ---- + 3/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 11, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 114, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 3, 34, 127, 591, 3516, 17403, 89559, 486223, 2563693, 13626768, 73395664,
394170076, 2123218527, 11485869489
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 115, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 67, 265, 1781, 13001, 75755, 509377, 3424153, 22171405, 148805075,
996671545, 6649852093, 44795141249, 301849584587
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 116, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 100, 415, 3571, 28576, 187237, 1492135, 11255167, 83425897, 646296982,
4920865984, 37636345072, 290615028991, 2236998217825
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 35, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 117, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 22, 103, 421, 1876, 8212, 36751, 164731, 744367, 3375802, 15375724,
70247932, 321870472, 1478312752
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 17, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 118, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 55, 301, 1941, 12051, 76539, 491653, 3172213, 20609749, 134486859,
880976911, 5790193891, 38161698927, 252127029345
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 22, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 119, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 88, 511, 4061, 29276, 216476, 1639023, 12344875, 93984811, 718288616,
5507806756, 42393510940, 327138855824, 2530654004708
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 120, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 121, 733, 6781, 53671, 440203, 3731701, 31129573, 264009433, 2244464773,
19134087919, 163865679199, 1406297414731, 12100128720511
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 30, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 121, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 49, 337, 1801, 11101, 65353, 398497, 2418961, 14842093, 91288033,
564173809, 3496652953, 21735716029, 135429712249
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 122, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 82, 607, 4311, 31536, 233535, 1743463, 13120255, 99267985, 754699320,
5759824720, 44104291180, 338667328455, 2606900765757
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 123, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 115, 889, 7421, 60101, 504827, 4240545, 35968201, 306713977, 2627331587,
22596482569, 194964688309, 1686946101725, 14631750660635
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 124, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 148, 1183, 11131, 96916, 891409, 8162743, 75430255, 701729869,
6551407534, 61437972256, 577905187120, 5451487479751, 51549534477733
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 35, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 125, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 82, 703, 4501, 33616, 239464, 1763119, 12954331, 96022099, 714380734,
5336114356, 39990027052, 300504579688, 2263719904192
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 17, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 126, : Let A(n) be the constant term, in x, of
/ 1 2\n
|1 + ---- + 3/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 21, 115, 1045, 8061, 67911, 563991, 4774869, 40568101, 347130241, 2982786951,
25735012711, 222755304331, 1933596302379, 16825136788845
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 21, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 127, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 23, 148, 1399, 12221, 111416, 1023968, 9495823, 88759435, 834019663,
7875349868, 74646026764, 709883092348, 6769870809872, 64719048195188
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 128, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 181, 1765, 16981, 164251, 1631575, 16219141, 163031509, 1645522885,
16695438145, 170022115495, 1737195291703, 17799551994823, 182818704607291
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 30, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 129, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 14, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 130, : Let A(n) be the constant term, in x, of
/ 1 2\n
|2 + ---- + 3/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 47, 286, 1602, 9699, 60132, 371214, 2307548, 14462626, 91035012,
574991971, 3644088086, 23160978000, 147557748987
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 50, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 131, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 86, 568, 3832, 29084, 215896, 1601632, 12091424, 91668448, 696993376,
5324668144, 40813043936, 313636507136, 2416170403936
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 15, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 132, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 125, 862, 6722, 58339, 480440, 4024990, 34336196, 292592410, 2506012280,
21575034595, 186221653022, 1611833827348, 13987050486065
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 133, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 47, 238, 1232, 6499, 34715, 187198, 1016840, 5555560, 30497150,
168073195, 929348396, 5153362231, 28646281502
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 25, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 134, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 86, 580, 4092, 29454, 214314, 1574500, 11652224, 86731012, 648619644,
4869770734, 36682896824, 277107171150, 2098432827606
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 14, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 135, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 125, 934, 7612, 63239, 527893, 4458990, 37932272, 324456424, 2788550998,
24059445931, 208264503332, 1807870237775, 15731693608750
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 136, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 164, 1300, 11792, 107974, 988472, 9194308, 86027960, 809204836,
7649884112, 72591979486, 691100890820, 6598091552446, 63145950761744
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 18, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 137, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 92, 616, 4112, 28144, 194672, 1359712, 9564608, 67668736, 480993152,
3432257536, 24572409344, 176415489280, 1269645293312
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 14, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 138, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 131, 1030, 8322, 68379, 569256, 4783678, 40494812, 344797498, 2949775116,
25335206659, 218324891150, 1886757094044, 16345408354311
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 139, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 20, 170, 1456, 13192, 120524, 1116880, 10446720, 98412704, 932492320,
8877227680, 84841358320, 813525505184, 7822772575232, 75406885390240
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 15, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 140, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 209, 1894, 18722, 184699, 1850564, 18722638, 190691300, 1953749362,
20110451264, 207809229379, 2154452620166, 22399057482208, 233442446848109
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 141, : Let A(n) be the constant term, in x, of
/ 1 \n
|2 + ---- + 3/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 143, 1150, 9032, 73099, 597179, 4926478, 40930136, 341993392, 2870906414,
24193487179, 204549937724, 1734265825699, 14739563348918
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 142, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 24, 182, 1636, 14652, 134574, 1249698, 11719908, 110707904, 1051886164,
10041899628, 96243953326, 925494049352, 8924981592726, 86279519856942
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 14, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 143, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 26, 221, 2134, 20932, 209039, 2115157, 21598462, 222173024, 2298591856,
23893662982, 249347367691, 2610737565620, 27412590681467, 288535722978646
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 144, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 28, 260, 2644, 27872, 296614, 3206576, 34956100, 383915672, 4240653748,
47061843776, 524325629854, 5860892884628, 65697830284870, 738240048624680
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 18, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 145, : Let A(n) be the constant term, in x, of
/ 1 \n
|3 + ---- + 3/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 21, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 146, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 72, 519, 3573, 24644, 173463, 1236391, 8870013, 63965061, 463456458,
3371364456, 24605785116, 180089790591, 1321295828067
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 35, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 147, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 117, 969, 7623, 62449, 523029, 4402561, 37283355, 317766933, 2721298869,
23392826169, 201748806639, 1744882927017, 15127859195397
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 148, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 162, 1431, 12393, 114264, 1064745, 9946071, 93723885, 888873345,
8466051960, 80944806600, 776511880992, 7470005128335, 72034992484227
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 149, : Let A(n) be the constant term, in x, of
/ 1 \n
|3 + ---- + 3/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 84, 495, 3003, 18564, 116280, 735471, 4686825, 30045015, 193536720,
1251677700, 8122425444, 52860229080, 344867425584
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 11, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 150, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 129, 1005, 7983, 64619, 530001, 4388645, 36608511, 307172637, 2589753741,
21920819919, 186169052241, 1585620914055, 13538300225319
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 22, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 151, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 174, 1527, 13683, 125644, 1167792, 10951887, 103467225, 983191059,
9386847462, 89971525356, 865223993988, 8344144919808, 80667564994164
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 152, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 219, 2061, 20103, 201759, 2043513, 20886357, 215095503, 2227784481,
23181720543, 242168099391, 2538160889085, 26677526149491, 281081075987229
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 30, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 153, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 147, 1089, 8283, 64149, 503163, 3984129, 31778355, 254950101, 2055118563,
16631351361, 135039238155, 1099575642837, 8975450076747
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 22, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 154, : Let A(n) be the constant term, in x, of
/ 1 2\n
|3 + ---- + 3/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 192, 1671, 14973, 136664, 1263699, 11798327, 110974989, 1050011433,
9982721994, 95287086024, 912593172780, 8765282582247, 84397758645087
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 34, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 155, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 237, 2265, 22383, 225229, 2294925, 23607201, 244625547, 2549708865,
26701907565, 280741645545, 2961531192519, 31330045673637, 332256772573437
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 156, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 282, 2871, 30513, 329964, 3610701, 39892071, 443946045, 4969177317,
55884278376, 630954015624, 7147318455072, 81192874716183, 924604690710327
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 157, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 216, 1863, 16443, 147744, 1344276, 12345615, 114202953, 1062534267,
9932277996, 93207429324, 877574192004, 8285942274840, 78425918957376
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 158, : Let A(n) be the constant term, in x, of
/ 1 2\n
|3 + ---- + 3/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 29, 261, 2517, 24903, 251039, 2563557, 26431477, 274548879, 2868644169,
30117280977, 317454892071, 3357408221001, 35609843787267, 378626397171291
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 21, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 159, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 31, 306, 3183, 34083, 371464, 4100988, 45707503, 513189945, 5795720631,
65766426498, 749233731156, 8564024112660, 98169292496544, 1128088286442756
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 160, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 33, 351, 3861, 43983, 509139, 5970429, 70675173, 842740767, 10107524493,
121801153059, 1473552741879, 17886314377701, 217724895110511,
2656812164068161
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 30, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 161, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2, 3}, never show up!
Theorem Number, 162, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 3, 24, 60, 175, 840, 1680, 10164, 20664, 115500, 281391, 1297296, 3838692,
14897883
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 163, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 6, 96, 240, 1340, 6720, 22400, 161952, 459648, 3622080, 10888944,
78414336, 272638080, 1691385696
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 6, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 164, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 9, 216, 540, 4455, 22680, 105840, 818748, 2980152, 27318060, 97037919,
875674800, 3421386540, 27672053409
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 165, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 2, 6, 6, 40, 80, 210, 742, 1680, 5292, 15180, 40524, 123552, 343772, 986986
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 166, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 9, 78, 240, 1335, 5355, 26110, 115668, 543816, 2499750, 11680251,
54478710, 255144175, 1198160964
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 32, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 167, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 12, 198, 560, 5020, 20580, 144774, 708960, 4486860, 23980440, 144874620,
809018496, 4792044400, 27372997652
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 168, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 15, 366, 1000, 12095, 50925, 454174, 2386860, 18396504, 108650850,
779959851, 4901037570, 34002807839, 220881360700
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 32, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 169, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 24, 24, 320, 1120, 3360, 22624, 75264, 330624, 1647360, 6141696, 28993536,
128567296, 531474944
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2, 3}, never show up!
Theorem Number, 170, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 27, 144, 900, 4175, 26460, 136640, 805140, 4489128, 25678620, 147274479,
842037768, 4863568424, 27995674707
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 171, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 30, 312, 1600, 11100, 71400, 458528, 3108000, 20083392, 136646400,
899829744, 6102233280, 40770878720, 276156680800
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 6, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 172, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 16, 33, 528, 2420, 22855, 143220, 1139488, 8072988, 60993576, 452043900,
3381052191, 25456211352, 190893946672, 1445604273113
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 15, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 173, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 54, 54, 1080, 5400, 17010, 168966, 734832, 3735396, 26462700, 121920876,
720555264, 4342096044, 22027599594
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 174, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 57, 222, 2280, 10975, 81795, 530670, 3381924, 23536800, 152618070,
1039404795, 6982162902, 47006723907, 319562335092
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 32, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 175, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 60, 438, 3600, 21860, 186900, 1255142, 9935520, 72688644, 553179000,
4194002076, 31747510080, 243010832064, 1850355807300
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 176, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 63, 702, 5040, 39015, 337365, 2547342, 22210524, 174808368, 1491453810,
12159698859, 102397032738, 851248720179, 7145398368108
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 177, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 6, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 178, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 16, 61, 251, 1016, 4355, 18621, 81205, 356155, 1573430, 6986200, 31140994,
139281455, 624616361
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 41, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 179, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 31, 169, 861, 4461, 24879, 134401, 761161, 4256689, 24262239, 138207961,
792787477, 4559039109, 26298912831
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 180, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 46, 325, 1831, 11296, 73333, 458221, 3058453, 19770643, 132459988,
876676384, 5889337390, 39487679167, 266278586041
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 181, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 3, 13, 43, 151, 561, 2073, 7715, 29011, 109633, 416043, 1585189, 6059353,
23224995, 89233693
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 182, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 28, 151, 781, 4216, 22912, 125903, 696619, 3876607, 21673972, 121646284,
684987772, 3867943184, 21894249748
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 183, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 43, 307, 1771, 11741, 75041, 496147, 3271363, 21799681, 145653641,
977889661, 6584131477, 44463245243, 300965380363
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 184, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 58, 511, 3121, 24096, 170220, 1283087, 9497587, 71685175, 540207570,
4100350420, 31177505308, 237913339392, 1819227859828
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 185, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 37, 145, 721, 3941, 19685, 101921, 539425, 2828485, 14942885, 79455025,
422942833, 2258151845, 12090801637
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 186, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 52, 301, 1971, 12396, 80739, 527437, 3472261, 23001919, 153016194,
1022072536, 6848799010, 46022234519, 310008304797
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 187, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 67, 505, 3581, 26161, 194923, 1453985, 10981417, 83169013, 633698803,
4844056009, 37158496597, 285810497545, 2203736079467
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 188, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 82, 757, 5551, 46196, 373997, 3099965, 25778917, 215711767, 1814123312,
15307993504, 129640671694, 1100704760039, 9369279969157
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 189, : Let A(n) be the constant term, in x, of
/ 2 \n
|1 + ---- + 1/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 73, 307, 1951, 13861, 81397, 523699, 3469123, 22152637, 144481327,
950666509, 6220704673, 40951593151, 270535280113
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 9, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 190, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 88, 511, 4061, 29276, 216476, 1639023, 12344875, 93984811, 718288616,
5507806756, 42393510940, 327138855824, 2530654004708
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 191, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 103, 763, 6531, 51441, 433245, 3598435, 30310771, 256550845, 2179900845,
18608015845, 159288912589, 1367623508343, 11769778788783
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 192, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 118, 1063, 9361, 81316, 743464, 6674095, 61288435, 561646819, 5188163014,
48049343596, 446613538060, 4162613091040, 38889202725028
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 193, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 194, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 35, 160, 772, 3839, 19546, 101280, 531764, 2820328, 15075436, 81076879,
438164534, 2377297784, 12939840475
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 195, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 62, 352, 2112, 12924, 81384, 520384, 3373856, 22095232, 145856064,
968879344, 6468148832, 43355525568, 291572336352
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 6, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 196, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 89, 592, 4052, 28279, 204122, 1489408, 11047292, 82683016, 624138572,
4740876991, 36196764086, 277510473088, 2134831686929
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 197, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 26, 118, 532, 2424, 11202, 52294, 245852, 1162276, 5520132, 26318956,
125894264, 603888172, 2903740306
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 198, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 53, 310, 1892, 11839, 75245, 483326, 3128768, 20375440, 133329110,
875909995, 5773461956, 38163131387, 252880464038
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 199, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 80, 550, 3852, 28004, 206908, 1548614, 11690252, 88826884, 678354448,
5201650876, 40021385432, 308804317696, 2388582610260
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 200, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 107, 838, 6412, 51879, 424671, 3533758, 29660408, 250787968, 2131747026,
18198477499, 155900165072, 1339453334587, 11536897514542
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 201, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 56, 328, 1872, 11264, 68896, 422496, 2608832, 16215808, 101245696,
634457344, 3988795904, 25147276288, 158919553536
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 202, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 83, 568, 4092, 29919, 221454, 1655056, 12458036, 94317592, 717428604,
5478493519, 41973619118, 322490785244, 2483811265323
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 203, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 110, 856, 6912, 56764, 473552, 3985888, 33802976, 288314176, 2470687232,
21254884336, 183453431072, 1587863444288, 13777051707360
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 6, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 204, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 20, 137, 1192, 10332, 92759, 843670, 7754352, 71825276, 669148600,
6263877820, 58863975295, 554990112926, 5247322710244, 49732947077217
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 205, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 98, 646, 4292, 31744, 232850, 1698022, 12567932, 93653980, 699652340,
5247942220, 39505205144, 298161175420, 2255610249458
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 206, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 125, 934, 7612, 63239, 527893, 4458990, 37932272, 324456424, 2788550998,
24059445931, 208264503332, 1807870237775, 15731693608750
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 207, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 152, 1270, 11532, 104364, 961116, 8930086, 83542796, 786199228,
7432817856, 70545012124, 671743016024, 6414432545616, 61400028720612
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 208, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 179, 1654, 16052, 156079, 1550999, 15504430, 156274568, 1583754712,
16125974834, 164835049339, 1690401666800, 17383950058063, 179208657048374
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 209, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 210, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 66, 357, 2013, 11704, 69639, 421773, 2590095, 16080003, 100696764,
634971984, 4026467682, 25649269239, 164004740211
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 211, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 105, 681, 4623, 32309, 230961, 1680065, 12388875, 92345337, 694259481,
5255535129, 40006451943, 305926461837, 2348176521105
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 212, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 144, 1053, 8073, 63504, 511353, 4187997, 34769007, 291769371, 2469513258,
21046597416, 180378463086, 1553020693623, 13421838407859
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 213, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 51, 267, 1453, 8009, 44523, 249475, 1407705, 7989561, 45561453,
260841381, 1498267683, 8630351531, 49834369891
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 214, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 90, 591, 4083, 29064, 210780, 1547695, 11464281, 85477095, 640576170,
4820411220, 36398556756, 275640152992, 2092580941860
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 215, : Let A(n) be the constant term, in x, of
/ 2 2\n
|3 + ---- + 1/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 129, 963, 7553, 61189, 506187, 4247091, 35990697, 307223289, 2637127947,
22735986381, 196719062751, 1707147542707, 14852303960369
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 11, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 216, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 168, 1383, 11863, 105344, 955944, 8807983, 82033377, 770071743,
7272174264, 68995741164, 657063780948, 6276730763312, 60115676023108
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 217, : Let A(n) be the constant term, in x, of
/ 2 \n
|3 + ---- + 1/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 87, 609, 4163, 28669, 200679, 1420225, 10119939, 72497133, 521739639,
3769359009, 27320908995, 198577505629, 1446808589447
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 218, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 126, 981, 7893, 64844, 539871, 4538333, 38433663, 327393927, 2802193056,
24079196304, 207602903394, 1794990074783, 15558234035031
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 219, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 165, 1401, 12463, 113529, 1050213, 9817313, 92480619, 876391101,
8344970373, 79774962441, 765156914343, 7359792205073, 70965068021365
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 220, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 204, 1869, 17873, 175684, 1756905, 17771245, 181242591, 1859938335,
19180826910, 198596982120, 2063136787182, 21493951800031, 224474815572719
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 221, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 135, 1107, 8613, 69309, 571455, 4741011, 39530025, 331582005, 2794975065,
23647888845, 200717858331, 1708381779399, 14575656833055
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 222, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 174, 1527, 13683, 125644, 1167792, 10951887, 103467225, 983191059,
9386847462, 89971525356, 865223993988, 8344144919808, 80667564994164
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 223, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 213, 1995, 19593, 195929, 1983999, 20284931, 208906809, 2163923253,
22520484759, 235295215989, 2466511223751, 25928668096431, 273236607114813
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 224, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 252, 2511, 26343, 281124, 3045276, 33307983, 367007841, 4067511147,
45292539636, 506315837124, 5678678950740, 63870003270576, 720120739050612
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 225, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 226, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 25, 97, 521, 2501, 12545, 64065, 325393, 1674565, 8636585, 44720545,
232429081, 1210941317, 6325164305
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 227, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 49, 241, 1761, 10041, 67089, 429409, 2785729, 18358249, 120259569,
796268881, 5272973473, 35045465625, 233510713809
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 228, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 73, 433, 3721, 23581, 190513, 1378273, 10517905, 80210413, 609407833,
4698123409, 36048870937, 278629449853, 2154641061313
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 229, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 19, 73, 301, 1241, 5195, 21953, 93385, 399565, 1717475, 7410745, 32080933,
139264529, 606012139
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 230, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 43, 265, 1581, 9741, 60579, 380353, 2405545, 15299089, 97761819,
627109561, 4035938245, 26047182149, 168512126883
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 231, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 67, 505, 3581, 26161, 194923, 1453985, 10981417, 83169013, 633698803,
4844056009, 37158496597, 285810497545, 2203736079467
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 232, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 91, 793, 6301, 51461, 435107, 3632609, 31014217, 263924857, 2266951787,
19502967529, 168496623829, 1459244026397, 12669561636931
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 233, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 49, 241, 1441, 8121, 46929, 275297, 1616449, 9568489, 56878449, 339316561,
2031216097, 12191914905, 73355518609
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 234, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 73, 529, 3721, 26941, 197233, 1456673, 10840465, 81117613, 609893593,
4603215409, 34857719833, 264699597917, 2014944995713
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 235, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 97, 865, 6721, 56561, 470177, 3982273, 33843841, 289684177, 2489672417,
21484861729, 185996101825, 1614743032241, 14052331289377
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 236, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 21, 121, 1249, 10441, 97941, 892641, 8349377, 78118033, 737035861,
6978684681, 66360270241, 632981525593, 6054915252309, 58058495769841
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 237, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 91, 505, 3901, 26641, 187363, 1358113, 9730153, 70618933, 514644043,
3759227209, 27578274517, 202798937641, 1494850486051
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 238, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 115, 889, 7421, 60101, 504827, 4240545, 35968201, 306713977, 2627331587,
22596482569, 194964688309, 1686946101725, 14631750660635
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 239, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 21, 139, 1321, 11661, 107241, 995331, 9311233, 87855817, 832941661,
7937381211, 75914930521, 728509774981, 7010399216289, 67625067981219
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 240, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 163, 1801, 16621, 169021, 1685755, 17174977, 175424617, 1805017825,
18647693395, 193433769145, 2012924810053, 21005971610677, 219738531772603
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 241, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 242, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 75, 465, 3003, 20029, 136419, 941985, 6567411, 46113453, 325553979,
2308301169, 16424559531, 117213313629, 838596904275
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 243, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 123, 897, 6963, 55889, 457131, 3791489, 31753059, 267811857, 2271082971,
19342185729, 165311886483, 1417029334353, 12177024531723
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 244, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 171, 1377, 12123, 109269, 1004643, 9374913, 88309683, 837885141,
7993601883, 76590962721, 736454791179, 7102209714453, 68664009249171
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 245, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 69, 393, 2303, 13729, 82869, 504961, 3099723, 19139733, 118747269,
739662009, 4622692311, 28973271193, 182042465189
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 246, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 117, 873, 6783, 53909, 434661, 3540161, 29052459, 239840217, 1989519381,
16569202329, 138455300727, 1160272014989, 9747281151477
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 247, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 165, 1401, 12463, 113529, 1050213, 9817313, 92480619, 876391101,
8344970373, 79774962441, 765156914343, 7359792205073, 70965068021365
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 248, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 213, 1977, 19343, 193549, 1969845, 20263777, 210108939, 2191759425,
22973774805, 241762494345, 2552615050599, 27027715134949, 286875624839333
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 249, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 123, 897, 6643, 50129, 383211, 2956417, 22971363, 179511057, 1409365851,
11108173569, 87838769619, 696545218001, 5536916176843
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 250, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 171, 1473, 13083, 118389, 1085283, 10044673, 93656115, 878386581,
8277708123, 78317021121, 743453353035, 7077691236469, 67546304093331
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 251, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 219, 2097, 20723, 208969, 2135115, 22025313, 228879075, 2392300665,
25123555515, 264882406545, 2801979624915, 29724048024745, 316093568851499
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 252, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 29, 267, 2769, 29563, 322829, 3573027, 39933217, 449598579, 5091390909,
57928915707, 661687723761, 7583049315819, 87148577826605, 1004007555520147
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 253, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 189, 1593, 13743, 121689, 1089693, 9840609, 89511723, 818863101,
7525639773, 69429995721, 642636244071, 5964774222897, 55497229084269
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 254, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 237, 2265, 22383, 225229, 2294925, 23607201, 244625547, 2549708865,
26701907565, 280741645545, 2961531192519, 31330045673637, 332256772573437
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 255, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 29, 285, 2985, 32223, 353969, 3938637, 44239169, 500533323, 5696099109,
65129071197, 747614001561, 8610311984823, 99446801724201, 1151402024923965
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 256, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 33, 333, 3753, 43263, 508869, 6061149, 72878913, 882668907, 10752276393,
131597190189, 1616928532569, 19932804539703, 246417800073597,
3053770977909933
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 257, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2, 3}, never show up!
Theorem Number, 258, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 27, 24, 540, 1375, 7560, 46480, 151956, 1028664, 4365900, 21269391,
115459344, 509303652, 2732997267
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 259, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 54, 96, 2160, 6140, 60480, 380800, 1941408, 16587648, 85821120, 630549744,
4026806784, 25057718400, 175879607904
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 6, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 260, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 81, 216, 4860, 15255, 204120, 1315440, 9001692, 84628152, 515300940,
4671075519, 33100507440, 257016808620, 2057492077641
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 261, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 6, 54, 120, 600, 1890, 7686, 27888, 106596, 405900, 1536876, 5930496,
22580844, 87393306
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 262, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 33, 222, 1320, 7375, 47355, 275310, 1736196, 10533600, 65706630,
407151195, 2540530278, 15886755027, 99530939508
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 263, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 60, 438, 3600, 21860, 186900, 1255142, 9935520, 72688644, 553179000,
4194002076, 31747510080, 243010832064, 1850355807300
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 264, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 87, 702, 6960, 45015, 465885, 3420942, 31646076, 260992368, 2266338690,
19641326859, 168546711762, 1476712358979, 12765083222892
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 32, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 265, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 24, 216, 960, 5280, 30240, 155232, 913920, 4862592, 28005120, 154623744,
877713408, 4942958592, 27981617664
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 3, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2, 3}, never show up!
Theorem Number, 266, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 16, 51, 528, 3060, 23935, 164220, 1219680, 8809332, 65106216, 479262300,
3556725711, 26425456200, 197088262800, 1472727467211
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 15, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 267, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 20, 78, 888, 6240, 54620, 447720, 3783584, 32192160, 273792960, 2354626560,
20223463920, 174881513664, 1513047169920, 13140216337248
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 6, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 268, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 24, 105, 1296, 10500, 98295, 926100, 8481984, 81711420, 763585704,
7355432700, 69944084991, 674045812440, 6476674525464, 62569963481025
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 269, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 54, 486, 3240, 19440, 153090, 949158, 7103376, 47947788, 342090540,
2413686924, 17023118112, 121627476828, 862150002714
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 270, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 22, 81, 942, 6480, 56455, 456435, 3829630, 32176116, 271455912, 2307734550,
19643430939, 168054990246, 1440139057071, 12379261890996
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 32, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 271, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 26, 108, 1446, 10800, 109820, 971460, 9359686, 87327072, 835927596,
7957022040, 76432242876, 734600161152, 7089753603504, 68541504539508
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 272, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 30, 135, 1998, 16200, 180495, 1743525, 18335646, 187075980, 1954040760,
20334179250, 213218995275, 2239378803090, 23600482604127, 249264553437900
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 32, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 273, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 274, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 40, 157, 971, 5576, 30395, 179005, 1031413, 5980315, 35100110, 205693720,
1211220466, 7155115007, 42338723705
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 275, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 79, 361, 3261, 21741, 154239, 1167489, 8350729, 62256049, 461728719,
3426137881, 25657449013, 191916851205, 1441012522959
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 276, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 118, 613, 6871, 49456, 423613, 3667693, 30117205, 262818163, 2235089308,
19251393184, 166733675902, 1440502088143, 12526084088713
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 277, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 25, 115, 511, 2341, 10837, 50611, 238147, 1126717, 5355967, 25557709,
122356417, 587411839, 2826889345
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 278, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 64, 415, 2861, 19436, 135836, 952239, 6735691, 47899531, 342216656,
2454572836, 17662711132, 127456452176, 921970893764
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 279, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 103, 763, 6531, 51441, 433245, 3598435, 30310771, 256550845, 2179900845,
18608015845, 159288912589, 1367623508343, 11769778788783
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 280, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 142, 1159, 11521, 99316, 955144, 8852719, 83961043, 798667459,
7620245854, 73134845356, 703218082828, 6785305011616, 65610936999172
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 281, : Let A(n) be the constant term, in x, of
/ 2 \n
|1 + ---- + 3/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 61, 385, 2401, 14941, 96013, 615553, 3993793, 26015533, 170310493,
1119220609, 7378509217, 48780642301, 323266358701
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 282, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 100, 829, 6371, 51476, 416627, 3415245, 28165861, 233706727, 1948038962,
16301553544, 136861333714, 1152270624935, 9724867347485
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 283, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 21, 139, 1321, 11661, 107241, 995331, 9311233, 87855817, 832941661,
7937381211, 75914930521, 728509774981, 7010399216289, 67625067981219
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 284, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 178, 1861, 18271, 183196, 1884205, 19328317, 201141637, 2097094975,
22004853520, 231614306320, 2446540491838, 25912508000887, 275122695839653
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 285, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 109, 811, 6391, 47521, 376489, 2937187, 23264659, 185072689, 1477981099,
11857932901, 95398253497, 769775390515, 6225910981309
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 286, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 23, 148, 1399, 12221, 111416, 1023968, 9495823, 88759435, 834019663,
7875349868, 74646026764, 709883092348, 6769870809872, 64719048195188
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 287, : Let A(n) be the constant term, in x, of
/ 2 2\n
|1 + ---- + 3/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 27, 187, 2035, 19371, 198861, 2021937, 20919123, 217314691, 2273060977,
23876367417, 251812893949, 2664297545365, 28269232393611, 300673258704027
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 11, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 288, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 31, 226, 2719, 27841, 310816, 3422476, 38393167, 432330643, 4901551111,
55810107706, 637990197076, 7316828619868, 84148498810624, 970111828316116
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 289, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 290, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 59, 352, 2212, 14639, 96826, 646048, 4350740, 29450728, 200260876,
1367195119, 9364357238, 64318682744, 442845544339
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 291, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 110, 736, 5952, 48444, 390504, 3222720, 26700320, 222282112, 1861053504,
15635874544, 131797101152, 1114112928192, 9440324644320
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 6, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 292, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 161, 1168, 11252, 102439, 939962, 8876032, 83484188, 792130696,
7553742572, 72246727711, 693579972854, 6676229315968, 64417508346041
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 293, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 50, 262, 1412, 7744, 43010, 241126, 1361660, 7733980, 44135060,
252851020, 1453385624, 8377694524, 48409438370
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 294, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 101, 742, 5692, 44279, 348973, 2776302, 22247120, 179305384, 1451969158,
11803779211, 96276318452, 787489979423, 6457021374286
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 295, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 152, 1270, 11532, 104364, 961116, 8930086, 83542796, 786199228,
7432817856, 70545012124, 671743016024, 6414432545616, 61400028720612
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 296, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 203, 1846, 18932, 188959, 1938239, 20009518, 207973544, 2175288472,
22850955074, 241001346139, 2550019889120, 27057140017951, 287788671418838
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 297, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 104, 712, 5072, 36544, 266912, 1967200, 14601920, 109006336, 817540352,
6155259136, 46494597632, 352187094016, 2674213712384
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 298, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 20, 155, 1336, 11692, 104399, 943630, 8610480, 79141844, 731648920,
6795953980, 63372712495, 592914790574, 5563039388612, 52323374287315
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 299, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 24, 206, 2008, 19872, 200124, 2042448, 21030496, 218145248, 2275699264,
23852014848, 250972308976, 2649449394464, 28048387826112, 297658339877856
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 6, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 300, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 28, 257, 2728, 29612, 324679, 3622166, 40695568, 460868828, 5247878968,
60040370876, 689576490079, 7945938584222, 91817719243852, 1063559968996217
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 301, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 170, 1366, 11732, 100504, 875954, 7700998, 68162012, 606845572,
5427408164, 48728213164, 438915525752, 3964510398892, 35895956728130
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 302, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 26, 221, 2134, 20932, 209039, 2115157, 21598462, 222173024, 2298591856,
23893662982, 249347367691, 2610737565620, 27412590681467, 288535722978646
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 303, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 30, 272, 2950, 31692, 349764, 3899100, 43901190, 497794700, 5677294180,
65052767760, 748317039100, 8636457510488, 99956164649280, 1159691439342132
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 304, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 34, 323, 3814, 44012, 523639, 6286583, 76238782, 931057496, 11436133984,
141127040738, 1748352464731, 21730705787936, 270856097780155,
3384226551825278
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 305, : Let A(n) be the constant term, in x, of
/ 2 \n
|3 + ---- + 3/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 9, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 306, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 90, 645, 4653, 34504, 260319, 1982605, 15208911, 117362403, 909971604,
7083182544, 55317783186, 433240911879, 3401389973475
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 307, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 153, 1257, 10863, 97589, 884481, 8094529, 74684619, 693009657,
6460682121, 60467597529, 567798150663, 5346695047053, 50470035911073
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 308, : Let A(n) be the constant term, in x, of
/ 2 2\n
|3 + ---- + 3/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 216, 1917, 18873, 190944, 1940193, 19985373, 207391023, 2163802491,
22686481458, 238781051496, 2521447504254, 26700633678663, 283430285883171
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 41, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 309, : Let A(n) be the constant term, in x, of
/ 2 \n
|3 + ---- + 3/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 87, 531, 3333, 21309, 138015, 902547, 5946153, 39406005, 262404585,
1754316045, 11767931451, 79165530375, 533883963567
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 9, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 310, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 150, 1239, 10563, 91804, 808272, 7184655, 64335993, 579488499,
5244519822, 47652399276, 434422880388, 3971722599360, 36401193762900
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 311, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 213, 1995, 19593, 195929, 1983999, 20284931, 208906809, 2163923253,
22520484759, 235295215989, 2466511223751, 25928668096431, 273236607114813
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 312, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 276, 2799, 30423, 334644, 3730716, 42007695, 476344257, 5432906187,
62255552076, 716166374724, 8265673738260, 95667463295088, 1109960564107476
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 313, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 159, 1233, 9843, 79989, 658143, 5465889, 45723363, 384694101, 3251864223,
27595902321, 234956883411, 2006117307957, 17170542663519
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 314, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 222, 2085, 20133, 198004, 1972575, 19840221, 201031647, 2048944815,
20983122240, 215740158720, 2225578627314, 23024747205807, 238791366352887
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 315, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 29, 285, 2985, 32223, 353969, 3938637, 44239169, 500533323, 5696099109,
65129071197, 747614001561, 8610311984823, 99446801724201, 1151402024923965
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 316, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 33, 348, 3933, 46113, 548844, 6621849, 80628333, 988897407, 12198777543,
151189535214, 1881150021144, 23483184599358, 293978478445167,
3689214649659183
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 317, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 243, 2187, 20493, 195129, 1880091, 18285507, 179113113, 1764495657,
17463682701, 173513183589, 1729616718339, 17289543598011, 173248733055843
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 318, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 31, 306, 3183, 34083, 371464, 4100988, 45707503, 513189945, 5795720631,
65766426498, 749233731156, 8564024112660, 98169292496544, 1128088286442756
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 319, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 35, 369, 4227, 49473, 590069, 7126395, 86884723, 1067042025, 13180777065,
163589364315, 2038335482445, 25482159109215, 319468518110595,
4014993050121249
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 320, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 39, 432, 5319, 66663, 851904, 11021832, 143944047, 1893563649, 25053740559,
333050216832, 4444732277676, 59513502554964, 799120028309040,
10756467370503972
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 321, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2, 3}, never show up!
Theorem Number, 322, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 3, 54, 90, 555, 1890, 6510, 34104, 89586, 568260, 1422531, 9081072,
24586848, 142705563
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 50, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 323, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 6, 216, 360, 4380, 15120, 97440, 544992, 2413152, 18073440, 67068144,
570810240, 2052198720, 17539538016
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 15, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 324, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 9, 486, 810, 14715, 51030, 481950, 2757888, 17176698, 136964520,
672962499, 6462480024, 28840975020, 295540974729
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 325, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 2, 9, 6, 60, 155, 315, 1582, 3780, 11592, 42570, 112299, 378378, 1219647,
3567564
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 326, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 12, 132, 440, 2870, 13020, 72100, 367248, 1945188, 10302600, 54299454,
290995848, 1542400574, 8295058772
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 17, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 327, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 15, 366, 1000, 12095, 50925, 454174, 2386860, 18396504, 108650850,
779959851, 4901037570, 34002807839, 220881360700
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 32, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 328, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 20, 18, 708, 1740, 31070, 125370, 1538404, 8172360, 82115460, 511269660,
4600061070, 31437204084, 265941660270, 1920529809198
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 329, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 36, 24, 480, 2320, 5040, 49504, 193536, 733824, 5005440, 19447296,
92911104, 519357696, 2165619456
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2, 3}, never show up!
Theorem Number, 330, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 39, 222, 1690, 8275, 62790, 355390, 2408952, 15154650, 97837740,
638712195, 4112747496, 26998857028, 175518862519
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 331, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 16, 42, 528, 3080, 23980, 182280, 1290688, 10362912, 74412576, 592653600,
4391928816, 34463677248, 261547329472, 2035429908512
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 15, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 332, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 22, 45, 942, 4650, 52675, 374850, 3427438, 28274400, 241966242, 2100819600,
17788547139, 156492198720, 1334189622480, 11749447034325
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 333, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 81, 54, 1620, 11475, 25515, 373086, 2020788, 8328096, 82996650, 419626251,
2347433946, 18626541219, 97173632556
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 334, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 84, 324, 4200, 21750, 185220, 1378020, 9654960, 77517972, 560138040,
4319736894, 32810561784, 248190577206, 1910801416524
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 17, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 335, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 87, 702, 6960, 45015, 465885, 3420942, 31646076, 260992368, 2266338690,
19641326859, 168546711762, 1476712358979, 12765083222892
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 32, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 336, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 24, 90, 1188, 9900, 84510, 878850, 7255332, 75547080, 661083444, 6606319500,
60934087566, 592462805220, 5628747475494, 54190076890950
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 337, : Let A(n) be the constant term, in x, of
/ 3 \n
|1 + ---- + 1/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 11, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 338, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 22, 103, 451, 2056, 9787, 46327, 225967, 1101577, 5443912, 26988424,
134633968, 673909159, 3384842377
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 339, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 43, 313, 1621, 10081, 61363, 376993, 2407705, 15119413, 97922683,
627764809, 4091742877, 26590711993, 174165850963
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 340, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 64, 631, 3511, 27316, 188749, 1382599, 10333279, 75965149, 581289094,
4350397096, 33513132628, 254794267495, 1968761839609
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 35, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 341, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 3, 16, 55, 201, 816, 3228, 12783, 51523, 208483, 845868, 3448204, 14103532,
57829656, 237701376
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 342, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 37, 229, 1301, 7851, 47559, 291397, 1799317, 11167669, 69666609,
436177831, 2740122295, 17260940503, 108998027147
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 30, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 343, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 58, 511, 3121, 24096, 170220, 1283087, 9497587, 71685175, 540207570,
4100350420, 31177505308, 237913339392, 1819227859828
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 344, : Let A(n) be the constant term, in x, of
/ 3 2\n
|1 + ---- + 1/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 21, 79, 901, 5661, 52791, 405231, 3559893, 29451877, 255226561, 2174624211,
18844082071, 162696419731, 1414476472059, 12299835495969
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 21, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 345, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 49, 193, 1001, 6341, 33545, 185473, 1082065, 6119365, 34861025, 201562945,
1161389113, 6707737349, 38929010489
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 346, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 70, 439, 3291, 22676, 165551, 1202055, 8807551, 64986901, 481075376,
3577692856, 26685660496, 199616797615, 1496806789125
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 347, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 91, 793, 6301, 51461, 435107, 3632609, 31014217, 263924857, 2266951787,
19502967529, 168496623829, 1459244026397, 12669561636931
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 348, : Let A(n) be the constant term, in x, of
/ 3 2\n
|1 + ---- + 1/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 23, 112, 1255, 10031, 95936, 876233, 8230615, 77749807, 736364713,
7033571678, 67234817464, 646177199812, 6219097620815, 60048264570317
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 34, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 349, : Let A(n) be the constant term, in x, of
/ 3 \n
|1 + ---- + 1/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 100, 415, 2761, 23716, 144712, 997711, 7478947, 51225967, 361809592,
2626630084, 18648796492, 133515159064, 965023408720
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 11, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 350, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 121, 733, 6781, 53671, 440203, 3731701, 31129573, 264009433, 2244464773,
19134087919, 163865679199, 1406297414731, 12100128720511
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 30, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 351, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 142, 1159, 11521, 99316, 955144, 8852719, 83961043, 798667459,
7620245854, 73134845356, 703218082828, 6785305011616, 65610936999172
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 352, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 163, 1693, 16981, 163891, 1723555, 17295685, 180988021, 1869009445,
19564502695, 204835762495, 2153989248139, 22710997599343, 239988664077733
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 22, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 353, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 13, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 354, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 47, 238, 1262, 6859, 38180, 216094, 1239860, 7190410, 42059360,
247728595, 1467332414, 8731277572, 52152609347
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 355, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 86, 568, 3752, 25564, 178712, 1265632, 9104288, 66121696, 484631072,
3576388336, 26546427104, 197976880768, 1482287736416
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 356, : Let A(n) be the constant term, in x, of
/ 3 2\n
|2 + ---- + 1/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 125, 1006, 7502, 59419, 478424, 3902350, 32394140, 270926962, 2290114004,
19475111539, 166678333382, 1433071275952, 12372546250745
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 50, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 357, : Let A(n) be the constant term, in x, of
/ 3 \n
|2 + ---- + 1/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 29, 142, 672, 3219, 15717, 77550, 385040, 1921936, 9638202, 48521851,
245067032, 1241182011, 6301307934
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 358, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 68, 436, 2912, 19974, 139344, 982916, 6989720, 50010292, 359558784,
2595408094, 18796855508, 136519262598, 993947615048
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 18, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 359, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 107, 838, 6412, 51879, 424671, 3533758, 29660408, 250787968, 2131747026,
18198477499, 155900165072, 1339453334587, 11536897514542
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 360, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 24, 146, 1348, 11172, 102174, 928398, 8664996, 81347888, 771280564,
7350394548, 70400755726, 676718565824, 6525297383622, 63082176105906
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 14, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 361, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 68, 424, 2512, 16304, 107536, 703840, 4646336, 30942208, 206824576,
1386962944, 9333271040, 62983963904, 426023964928
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 13, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 362, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 107, 790, 6302, 50579, 411448, 3380654, 27966932, 232713394, 1945471288,
16327320211, 137477812214, 1160835229064, 9825733252727
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 363, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 20, 146, 1264, 11352, 103244, 958960, 8968320, 84596384, 802320160,
7645836640, 73144257520, 702033937568, 6756986492416, 65192852813856
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 364, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 26, 185, 1846, 17662, 177539, 1806772, 18583198, 192860636, 2012340826,
21106421932, 222208073971, 2347314722222, 24864956335028, 264035557782685
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 365, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 125, 862, 5912, 48619, 386885, 3008926, 24068960, 194053480, 1561400810,
12627434395, 102591165224, 835140360799, 6813604010870
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 25, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 366, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 164, 1300, 11792, 107974, 988472, 9194308, 86027960, 809204836,
7649884112, 72591979486, 691100890820, 6598091552446, 63145950761744
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 18, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 367, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 203, 1846, 18932, 188959, 1938239, 20009518, 207973544, 2175288472,
22850955074, 241001346139, 2550019889120, 27057140017951, 287788671418838
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 368, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 28, 242, 2500, 27332, 294814, 3292886, 36752356, 414831536, 4703094628,
53584658756, 612873962254, 7032350024624, 80919979013566, 933370060110362
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 14, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 369, : Let A(n) be the constant term, in x, of
/ 3 \n
|3 + ---- + 1/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 21, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 370, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 84, 495, 3033, 19104, 122895, 803847, 5328669, 35709345, 241439850,
1644448320, 11268599904, 77609985111, 536792233659
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 35, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 371, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 141, 1017, 7623, 58569, 459693, 3666273, 29628123, 242007741, 1994256333,
16553858121, 138245736879, 1160397425313, 9781658699421
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 372, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 198, 1647, 14013, 122364, 1091961, 9891639, 90813069, 842480757,
7885027296, 74336316624, 705086271828, 6722010765063, 64361259732123
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 373, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 54, 303, 1743, 10064, 58488, 342799, 2024433, 12027051, 71788698,
430155636, 2585884356, 15588611112, 94201873344
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 17, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 374, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 111, 789, 5903, 45539, 358221, 2854693, 22958175, 185888637, 1513000371,
12366428919, 101425821669, 834286694783, 6879610345841
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 30, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 375, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 168, 1383, 11863, 105344, 955944, 8807983, 82033377, 770071743,
7272174264, 68995741164, 657063780948, 6276730763312, 60115676023108
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 376, : Let A(n) be the constant term, in x, of
/ 3 2\n
|3 + ---- + 1/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 29, 225, 2085, 19623, 192719, 1931037, 19681909, 202928463, 2110665609,
22097546397, 232534965111, 2456944843473, 26045817852531, 276868300728015
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 21, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 377, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 99, 753, 5403, 39229, 291819, 2195041, 16597683, 126137133, 963202419,
7384086609, 56789615691, 437959781853, 3385645890939
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 22, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 378, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 156, 1311, 11473, 102604, 929547, 8503063, 78356685, 726274989,
6763643802, 63236216976, 593184569760, 5580127723231, 52621419169831
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 35, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 379, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 213, 1977, 19343, 193549, 1969845, 20263777, 210108939, 2191759425,
22973774805, 241762494345, 2552615050599, 27027715134949, 286875624839333
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 380, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 31, 270, 2751, 29013, 315304, 3492093, 39137863, 442540989, 5036148801,
57602792448, 661537608576, 7623091184868, 88094071532463, 1020533368904415
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 381, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 1/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 162, 1431, 11583, 99684, 886140, 7864047, 70025553, 628467255,
5669425710, 51312837420, 465873751476, 4241819032200, 38714898642192
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 17, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 382, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 219, 2061, 20103, 201759, 2043513, 20886357, 215095503, 2227784481,
23181720543, 242168099391, 2538160889085, 26677526149491, 281081075987229
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 30, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 383, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 276, 2799, 30423, 334644, 3730716, 42007695, 476344257, 5432906187,
62255552076, 716166374724, 8265673738260, 95667463295088, 1109960564107476
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 384, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 1/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 33, 333, 3645, 42543, 501579, 6027129, 73070181, 892691199, 10969766253,
135434923209, 1678652780319, 20874498339321, 260310127316391,
3254026087212363
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 22, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 385, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2, 3}, never show up!
Theorem Number, 386, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 12, 54, 360, 780, 7560, 19110, 141456, 514836, 2688840, 12775356,
55783728, 293775768, 1254965712
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 387, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 24, 216, 1440, 5280, 60480, 198240, 2220288, 9217152, 78946560,
428338944, 2905943040, 18839208960, 113845315584
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2, 3}, never show up!
Theorem Number, 388, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 36, 486, 3240, 16740, 204120, 822150, 11167632, 51621948, 581537880,
3411250524, 30578564016, 218380785480, 1679415834096
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 389, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 9, 24, 120, 295, 1260, 4144, 14364, 53424, 182160, 669471, 2378376,
8547396, 30999969
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 390, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 21, 222, 910, 6475, 33810, 214270, 1226568, 7519050, 44643060, 271738995,
1639421784, 9987222388, 60747067381
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 391, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 16, 33, 528, 2420, 22855, 143220, 1139488, 8072988, 60993576, 452043900,
3381052191, 25456211352, 190893946672, 1445604273113
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 15, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 392, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 22, 45, 942, 4650, 52675, 374850, 3427438, 28274400, 241966242, 2100819600,
17788547139, 156492198720, 1334189622480, 11749447034325
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 393, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 36, 96, 960, 3440, 20160, 114688, 532224, 3161088, 16220160, 87039744,
482347008, 2547038208, 14031553536
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2, 3}, never show up!
Theorem Number, 394, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 48, 438, 2720, 19340, 137760, 964390, 7017024, 50038884, 364980000,
2642109756, 19317355200, 141107646680, 1035194608448
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 395, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 20, 60, 888, 5200, 51920, 386400, 3447136, 28049280, 242645760, 2043888000,
17583244800, 150328189440, 1295381914112, 11159026278400
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 2, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2, 3}, never show up!
Theorem Number, 396, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 26, 72, 1446, 8400, 104420, 811440, 8573446, 75364128, 751104396, 6967485360,
68083216476, 647328341088, 6292354400904, 60564396084192
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 397, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 81, 216, 3240, 15255, 102060, 825552, 4592700, 35026992, 236720880,
1553288319, 11281193352, 75436882092, 525411447561
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 398, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 93, 702, 6510, 45195, 410130, 3196830, 27180552, 225560538, 1888355700,
15956447859, 134330645592, 1140101509404, 9668650244253
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 399, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 24, 105, 1296, 10500, 98295, 926100, 8481984, 81711420, 763585704,
7355432700, 69944084991, 674045812440, 6476674525464, 62569963481025
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 400, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 30, 117, 1998, 15210, 177795, 1695330, 18054414, 185159520, 1940517810,
20368473840, 214148236995, 2267127061056, 23981812466040, 255038251745277
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 401, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 402, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 31, 139, 811, 4081, 23017, 126211, 704515, 3964117, 22326877, 126623509,
719388853, 4101044143, 23432673271
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 403, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 61, 385, 2881, 17821, 136333, 927361, 6836353, 49118893, 358299613,
2624654209, 19225786945, 141731035837, 1044701312941
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 404, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 91, 739, 6211, 44461, 407989, 3141811, 27794611, 229228489, 1976011489,
16840543501, 144475141357, 1245842151139, 10729407983131
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 405, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 22, 85, 371, 1616, 7085, 31501, 140845, 633235, 2860760, 12972400,
59015698, 269229455, 1231171037
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 36, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 406, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 52, 367, 2331, 15836, 106961, 734007, 5060815, 35122741, 244814846,
1713217936, 12027863056, 84680593687, 597624238677
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 35, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 407, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 82, 757, 5551, 46196, 373997, 3099965, 25778917, 215711767, 1814123312,
15307993504, 129640671694, 1100704760039, 9369279969157
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 408, : Let A(n) be the constant term, in x, of
/ 3 2\n
|1 + ---- + 2/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 23, 112, 1255, 10031, 95936, 876233, 8230615, 77749807, 736364713,
7033571678, 67234817464, 646177199812, 6219097620815, 60048264570317
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 34, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 409, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 61, 289, 1881, 11481, 69189, 435009, 2715505, 17052649, 107911629,
684134881, 4353063625, 27780372153, 177671688021
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 410, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 91, 715, 5531, 43401, 347565, 2794051, 22682899, 184983085, 1516274145,
12474913045, 102976097173, 852405168343, 7073074138691
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 411, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 21, 121, 1249, 10441, 97941, 892641, 8349377, 78118033, 737035861,
6978684681, 66360270241, 632981525593, 6054915252309, 58058495769841
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 412, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 27, 151, 1891, 16611, 178341, 1772457, 18565107, 191755843, 2012282017,
21109667877, 222836425549, 2357192730205, 25018285817643, 266101374484791
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 413, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 118, 613, 5251, 39736, 287533, 2270605, 17420941, 134426683, 1053142168,
8222381344, 64507816738, 508027777375, 4005588284893
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 36, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 414, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 148, 1183, 11131, 96916, 891409, 8162743, 75430255, 701729869,
6551407534, 61437972256, 577905187120, 5451487479751, 51549534477733
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 35, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 415, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 178, 1861, 18271, 183196, 1884205, 19328317, 201141637, 2097094975,
22004853520, 231614306320, 2446540491838, 25912508000887, 275122695839653
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 416, : Let A(n) be the constant term, in x, of
/ 3 2\n
|1 + ---- + 2/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 31, 208, 2647, 26671, 301816, 3333961, 37594327, 425795023, 4849606081,
55526229166, 637836174856, 7353643604932, 84996955243903, 984936321078013
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 34, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 417, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 418, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 56, 310, 1892, 11764, 74720, 481702, 3134396, 20545420, 135412400,
896364220, 5954542856, 39672766696, 264987737216
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 419, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 104, 712, 5552, 42304, 337472, 2709088, 22004672, 180130816, 1482313472,
12256066816, 101691700736, 846323488768, 7061334370304
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 420, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 152, 1222, 11012, 94924, 879104, 8055814, 75377276, 708583732,
6702934064, 63721287964, 607792062152, 5816336101528, 55797203442752
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 421, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 41, 208, 1072, 5639, 30046, 161536, 874652, 4763008, 26058496, 143119519,
788623214, 4357696568, 24137804161
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 422, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 89, 646, 4802, 36539, 281668, 2192558, 17192420, 135593314, 1074441568,
8547195331, 68217505670, 545999650616, 4380746574869
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 423, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 20, 137, 1192, 10332, 92759, 843670, 7754352, 71825276, 669148600,
6263877820, 58863975295, 554990112926, 5247322710244, 49732947077217
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 424, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 26, 185, 1846, 17662, 177539, 1806772, 18583198, 192860636, 2012340826,
21106421932, 222208073971, 2347314722222, 24864956335028, 264035557782685
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 425, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 92, 592, 4032, 28464, 201504, 1439232, 10364672, 75039232, 545731584,
3984342784, 29183499776, 214347856896, 1578137951232
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 426, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 140, 1174, 10172, 89364, 796056, 7155110, 64782572, 589921948,
5397220776, 49572508924, 456817283288, 4221516171240, 39106924773680
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 427, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 24, 188, 1864, 18112, 182064, 1845888, 18912352, 195108416, 2024531584,
21105295488, 220874146816, 2319108947456, 24418300664320, 257729407433728
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 4, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 428, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 30, 236, 2662, 27852, 309804, 3441720, 38810118, 439975820, 5020019140,
57530213160, 661921766620, 7640502079160, 88441612221720, 1026220606945776
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 5, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 429, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 161, 1168, 9632, 82999, 701822, 6027424, 52294652, 455128576, 3980529632,
34957736191, 307936960814, 2720091434272, 24085600569881
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 430, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 209, 1894, 18722, 184699, 1850564, 18722638, 190691300, 1953749362,
20110451264, 207809229379, 2154452620166, 22399057482208, 233442446848109
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 431, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 28, 257, 2728, 29612, 324679, 3622166, 40695568, 460868828, 5247878968,
60040370876, 689576490079, 7945938584222, 91817719243852, 1063559968996217
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 432, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 34, 305, 3670, 42302, 506179, 6107348, 74408254, 913231772, 11270061034,
139746563948, 1739450879731, 21722649705902, 272034802759516,
3414991429703285
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 433, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 434, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 93, 603, 4113, 29049, 209835, 1539939, 11430345, 85551885, 644363415,
4877033445, 37057558671, 282479087367, 2159021017653
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 435, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 159, 1233, 10323, 88629, 779103, 6960417, 62887587, 573028821,
5254737183, 48425629041, 448037751411, 4158668284533, 38704583832159
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 436, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 225, 1971, 18873, 182709, 1823391, 18457875, 189056025, 1953345537,
20311790931, 212286973149, 2227601718423, 23451644875707, 247566248826705
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 437, : Let A(n) be the constant term, in x, of
/ 3 \n
|3 + ---- + 2/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 72, 429, 2613, 16144, 100929, 636925, 4048839, 25887483, 166302414,
1072532184, 6940009170, 45033929079, 292943440647
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 35, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 438, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 138, 1095, 9073, 77044, 664317, 5788519, 50829213, 449013069, 3985601832,
35518288056, 317584289376, 2847755324839, 25598520695623
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 439, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 204, 1869, 17873, 175684, 1756905, 17771245, 181242591, 1859938335,
19180826910, 198596982120, 2063136787182, 21493951800031, 224474815572719
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 440, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 31, 270, 2751, 29013, 315304, 3492093, 39137863, 442540989, 5036148801,
57602792448, 661537608576, 7623091184868, 88094071532463, 1020533368904415
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 441, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 2/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 135, 1041, 8043, 63569, 509631, 4120993, 33553683, 274761297, 2260414071,
18667758129, 154671536763, 1285110440337, 10703354414895
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 442, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 201, 1851, 17633, 171089, 1681599, 16685923, 166785177, 1676848293,
16939092459, 171789670149, 1748022315471, 17837360202671, 182465597624561
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 443, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 29, 267, 2769, 29563, 322829, 3573027, 39933217, 449598579, 5091390909,
57928915707, 661687723761, 7583049315819, 87148577826605, 1004007555520147
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 444, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 35, 333, 3795, 43833, 522029, 6297315, 76778515, 943058025, 11651905305,
144645447015, 1802646808125, 22539573912807, 282619738055235,
3552351378345693
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 445, : Let A(n) be the constant term, in x, of
/ 3 \n
|3 + ---- + 2/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 216, 1917, 17253, 161784, 1531953, 14596605, 140153895, 1353650211,
13132484478, 127891753416, 1249543617858, 12242332028871, 120231780433191
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 35, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 446, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 282, 2871, 30513, 329964, 3610701, 39892071, 443946045, 4969177317,
55884278376, 630954015624, 7147318455072, 81192874716183, 924604690710327
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 447, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 33, 348, 3933, 46113, 548844, 6621849, 80628333, 988897407, 12198777543,
151189535214, 1881150021144, 23483184599358, 293978478445167,
3689214649659183
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 42, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 448, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 2/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 39, 414, 5103, 64053, 821664, 10678797, 140083911, 1851108957, 24601398489,
328492431072, 4403316869136, 59219110694916, 798665316014367,
10797531402095919
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 449, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 3/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 450, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 46, 199, 1411, 8056, 49267, 309751, 1901935, 11977417, 75228352,
474478984, 3007561168, 19088361943, 121528903321
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 451, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 91, 505, 4981, 33121, 278083, 2180641, 17214553, 140291893, 1120096363,
9118057609, 73972081405, 602505781177, 4924434083491
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 452, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 136, 919, 10711, 78436, 811189, 7132231, 66785311, 631180189, 5847324814,
55736022376, 524057651092, 4984321672279, 47380317974281
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 35, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 453, : Let A(n) be the constant term, in x, of
/ 3 \n
|1 + ---- + 3/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 28, 127, 601, 2836, 13672, 66319, 324163, 1593487, 7868752, 39007684,
193998988, 967517656, 4836876688
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 11, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 454, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 73, 541, 3901, 28711, 215083, 1618933, 12302821, 93920473, 720669973,
5550284719, 42888269503, 332329270027, 2581379971183
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 30, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 455, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 118, 1063, 9361, 81316, 743464, 6674095, 61288435, 561646819, 5188163014,
48049343596, 446613538060, 4162613091040, 38889202725028
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 456, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 163, 1693, 16981, 163891, 1723555, 17295685, 180988021, 1869009445,
19564502695, 204835762495, 2153989248139, 22710997599343, 239988664077733
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 22, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 457, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 3/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 73, 433, 3001, 19261, 130033, 878305, 5963761, 40837933, 280474393,
1934740369, 13388260393, 92896734685, 646162569793
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2, 3}, never show up!
Theorem Number, 458, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 118, 1063, 8731, 75916, 659359, 5805703, 51411295, 458084269, 4100076784,
36841864456, 332129714320, 3002567395231, 27210163458133
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 47, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 459, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 163, 1801, 16621, 169021, 1685755, 17174977, 175424617, 1805017825,
18647693395, 193433769145, 2012924810053, 21005971610677, 219738531772603
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 460, : Let A(n) be the constant term, in x, of
/ 3 2\n
|1 + ---- + 3/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 31, 208, 2647, 26671, 301816, 3333961, 37594327, 425795023, 4849606081,
55526229166, 637836174856, 7353643604932, 84996955243903, 984936321078013
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 34, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 461, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 3/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 136, 919, 8281, 63856, 530524, 4424239, 36718435, 309538099, 2609332804,
22100968396, 187876087660, 1600637137048, 13673650194496
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 12, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {2}, never show up!
Theorem Number, 462, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 181, 1765, 16981, 164251, 1631575, 16219141, 163031509, 1645522885,
16695438145, 170022115495, 1737195291703, 17799551994823, 182818704607291
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 30, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 463, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 31, 226, 2719, 27841, 310816, 3422476, 38393167, 432330643, 4901551111,
55810107706, 637990197076, 7316828619868, 84148498810624, 970111828316116
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 464, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 37, 271, 3781, 40861, 506791, 6027967, 74098837, 907716133, 11235051217,
139416470227, 1738293567319, 21735574815475, 272588760670123,
3426566851657441
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 22, states .
For example, A(100000), mudolo , 4, equals , 1
The congruence classes mod, 4, in the following set , {0, 2}, never show up!
Theorem Number, 465, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 3/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 13, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 466, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 71, 430, 2942, 20539, 144020, 1025182, 7346996, 52942570, 383400800,
2787170995, 20328011966, 148678494436, 1090065392891
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 467, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 134, 952, 8552, 72604, 635672, 5652448, 50332832, 452264416, 4079466272,
36940159216, 335653543136, 3058081779328, 27930195838304
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 468, : Let A(n) be the constant term, in x, of
/ 3 2\n
|2 + ---- + 3/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 197, 1582, 16862, 159499, 1622504, 16490254, 168244316, 1736707282,
17949522164, 186508941139, 1943706569222, 20311508666128, 212793921527777
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 50, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 469, : Let A(n) be the constant term, in x, of
/ 3 \n
|2 + ---- + 3/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 53, 286, 1592, 9019, 51725, 299422, 1745792, 10237480, 60315290,
356740795, 2116928504, 12597419215, 75147483158
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 470, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 116, 916, 7472, 61894, 519752, 4404292, 37594232, 322745956, 2783809712,
24105317086, 209419347620, 1824503882686, 15934258258496
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 18, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 471, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 179, 1654, 16052, 156079, 1550999, 15504430, 156274568, 1583754712,
16125974834, 164835049339, 1690401666800, 17383950058063, 179208657048374
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 472, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 28, 242, 2500, 27332, 294814, 3292886, 36752356, 414831536, 4703094628,
53584658756, 612873962254, 7032350024624, 80919979013566, 933370060110362
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 14, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 473, : Let A(n) be the constant term, in x, of
/ 3 \n
|---- + 3/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 116, 808, 6032, 45424, 345872, 2660704, 20606912, 160504576, 1255970432,
9865916416, 77751386624, 614452786432, 4867614976256
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 13, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 474, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 179, 1654, 15422, 146899, 1415864, 13776718, 135021140, 1330957762,
13181632664, 131060482579, 1307396822006, 13078832786608, 131156898478559
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 59, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 475, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 28, 242, 2608, 27512, 299404, 3287216, 36460288, 407220128, 4574510368,
51627802976, 584937681904, 6649057311392, 75793079942272, 866072413378592
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 476, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 34, 305, 3670, 42302, 506179, 6107348, 74408254, 913231772, 11270061034,
139746563948, 1739450879731, 21722649705902, 272034802759516,
3414991429703285
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 4, equals , 2
all the congruences classes mod, 4, show up
Theorem Number, 477, : Let A(n) be the constant term, in x, of
/ 3 \n
|2 + ---- + 3/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 197, 1582, 14432, 130339, 1188749, 10992622, 102170672, 955182832,
8972492234, 84596753179, 800223519656, 7590561630331, 72173424715982
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 24, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 478, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 28, 260, 2644, 27872, 296614, 3206576, 34956100, 383915672, 4240653748,
47061843776, 524325629854, 5860892884628, 65697830284870, 738240048624680
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 18, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
Theorem Number, 479, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 34, 323, 3814, 44012, 523639, 6286583, 76238782, 931057496, 11436133984,
141127040738, 1748352464731, 21730705787936, 270856097780155,
3384226551825278
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 31, states .
For example, A(100000), mudolo , 4, equals , 0
all the congruences classes mod, 4, show up
Theorem Number, 480, : Let A(n) be the constant term, in x, of
/ 3 2\n
|---- + 3/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 40, 386, 5092, 62852, 814654, 10576190, 139081828, 1839831920, 24487567540,
327396267860, 4394457784270, 59176751771360, 799127466216070,
10817660930841026
We are interested in A(n) modulo , 4
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 14, states .
For example, A(100000), mudolo , 4, equals , 0
The congruence classes mod, 4, in the following set , {3}, never show up!
This ends this fascinating book that took, 4.573, to generate.
----------------------------------------------------------
--------------------------------------
On computing the Mod, 8, of Many Interesting sequences
by Shalosh B. Ekhad
Theorem Number, 1, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 68, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 6, 7},
never show up!
Theorem Number, 2, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 23, 94, 402, 1779, 8052, 37006, 171932, 805186, 3793572, 17957251,
85323734, 406676976, 1943412483
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 586, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 3, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 38, 184, 952, 5084, 27736, 153696, 860960, 4861408, 27616096, 157617904,
903002336, 5189453312, 29901183328
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 81, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 4, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 53, 286, 1682, 10099, 62120, 388126, 2451140, 15606970, 99979640,
643535875, 4158061598, 26950603060, 175140491273
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 643, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 5, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 23, 94, 392, 1659, 7107, 30734, 133880, 586576, 2582142, 11411371,
50597900, 224986467, 1002867878
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 250, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 6, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 38, 196, 1052, 5774, 32146, 180772, 1024256, 5837908, 33433996, 192239854,
1109049320, 6416509142, 37215072638
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 99, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 7, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 53, 310, 1892, 11839, 75245, 483326, 3128768, 20375440, 133329110,
875909995, 5773461956, 38163131387, 252880464038
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 294, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 8, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 68, 436, 2912, 19974, 139344, 982916, 6989720, 50010292, 359558784,
2595408094, 18796855508, 136519262598, 993947615048
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 114, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 9, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 44, 232, 1232, 6704, 36976, 205664, 1151936, 6489088, 36724096, 208635904,
1189162496, 6796807424, 38941961984
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 66, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 6, 7},
never show up!
Theorem Number, 10, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 59, 358, 2242, 14299, 92360, 602270, 3956252, 26140330, 173541260,
1156667395, 7734994958, 51873729652, 348741401119
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 590, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 11, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 74, 496, 3432, 24204, 172944, 1247488, 9064352, 66245152, 486431904,
3585858544, 26521709216, 196715685248, 1462647306144
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 74, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 6, 7},
never show up!
Theorem Number, 12, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 89, 646, 4802, 36539, 281668, 2192558, 17192420, 135593314, 1074441568,
8547195331, 68217505670, 545999650616, 4380746574869
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 631, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 13, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 71, 430, 2672, 17299, 112835, 740926, 4904360, 32649640, 218325230,
1465532875, 9869605436, 66650927815, 451185626366
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 254, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 14, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 86, 580, 4092, 29454, 214314, 1574500, 11652224, 86731012, 648619644,
4869770734, 36682896824, 277107171150, 2098432827606
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 88, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 15, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 101, 742, 5692, 44279, 348973, 2776302, 22247120, 179305384, 1451969158,
11803779211, 96276318452, 787489979423, 6457021374286
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 294, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 16, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 116, 916, 7472, 61894, 519752, 4404292, 37594232, 322745956, 2783809712,
24105317086, 209419347620, 1824503882686, 15934258258496
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 134, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 17, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 112, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 5, 6, 7},
never show up!
Theorem Number, 18, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 48, 231, 1173, 6164, 33183, 181799, 1008957, 5653701, 31912818,
181156776, 1032969564, 5911392015, 33930026163
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 515, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 19, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 69, 393, 2343, 14449, 91269, 586497, 3816411, 25066773, 165813189,
1102873209, 7367533839, 49390996521, 332074347189
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 230, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 20, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 90, 567, 3753, 25704, 180225, 1285335, 9281709, 67649985, 496555920,
3664741320, 27164429568, 202060317663, 1507366068435
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 560, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 21, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 48, 231, 1163, 5984, 31188, 164047, 869097, 4631211, 24797028, 133302156,
719013636, 3889437080, 21091925888
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 81, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 22, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 69, 405, 2503, 15919, 103029, 674613, 4454223, 29596473, 197645649,
1325302119, 8917233705, 60174146899, 407079536539
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 216, states .
For example, A(100000), mudolo , 8, equals , 5
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 23, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 90, 591, 4083, 29064, 210780, 1547695, 11464281, 85477095, 640576170,
4820411220, 36398556756, 275640152992, 2092580941860
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 115, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 24, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 111, 789, 5903, 45539, 358221, 2854693, 22958175, 185888637, 1513000371,
12366428919, 101425821669, 834286694783, 6879610345841
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 284, states .
For example, A(100000), mudolo , 8, equals , 5
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 25, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 1/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 75, 465, 2923, 18589, 119619, 777121, 5085651, 33473133, 221347899,
1469414769, 9786831291, 65367631741, 437665012915
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 166, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 26, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 96, 663, 4733, 34464, 254355, 1895735, 14235693, 107538705, 816302490,
6221251320, 47574051372, 364849702967, 2805038513231
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 498, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 27, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 117, 873, 6783, 53909, 434661, 3540161, 29052459, 239840217, 1989519381,
16569202329, 138455300727, 1160272014989, 9747281151477
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 230, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 28, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 138, 1095, 9073, 77044, 664317, 5788519, 50829213, 449013069, 3985601832,
35518288056, 317584289376, 2847755324839, 25598520695623
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 590, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 29, : Let A(n) be the constant term, in x, of
/ 1 \n
|3 + ---- + 1/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 108, 783, 5643, 41364, 307800, 2311983, 17485065, 132980535, 1016080200,
7793724420, 59975964324, 462830103576, 3580271880048
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 72, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 30, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 129, 1005, 7983, 64619, 530001, 4388645, 36608511, 307172637, 2589753741,
21920819919, 186169052241, 1585620914055, 13538300225319
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 216, states .
For example, A(100000), mudolo , 8, equals , 5
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 31, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 150, 1239, 10563, 91804, 808272, 7184655, 64335993, 579488499,
5244519822, 47652399276, 434422880388, 3971722599360, 36401193762900
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 119, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 32, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 1/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 171, 1485, 13383, 123039, 1146393, 10784853, 102210255, 974339361,
9332293743, 89738353791, 865787580765, 8376809358771, 81248052512781
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 304, states .
For example, A(100000), mudolo , 8, equals , 5
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 33, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 4, 5, 6, 7},
never show up!
Theorem Number, 34, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 2, 12, 6, 120, 260, 840, 4550, 10416, 50652, 175560, 571164, 2450448,
7979400, 30702672
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 23, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 35, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 24, 24, 480, 1120, 6720, 36960, 123648, 814464, 3252480, 16279296,
83026944, 363297792, 1912694784
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 11, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 5, 6, 7},
never show up!
Theorem Number, 36, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 36, 54, 1080, 2700, 22680, 126630, 553392, 4143636, 18711000, 118713276,
665512848, 3580258968, 21938572656
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 5, 7},
never show up!
Theorem Number, 37, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 3, 24, 40, 175, 420, 1456, 4116, 13104, 39600, 122991, 380952, 1180036,
3686683
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 107, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 38, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 15, 78, 350, 1515, 7350, 32942, 157920, 734706, 3498000, 16578771,
79073280, 377947856, 1810383575
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 629, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 39, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 27, 144, 900, 4175, 26460, 136640, 805140, 4489128, 25678620, 147274479,
842037768, 4863568424, 27995674707
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 127, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 40, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 39, 222, 1690, 8275, 62790, 355390, 2408952, 15154650, 97837740,
638712195, 4112747496, 26998857028, 175518862519
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 613, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 41, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 12, 96, 320, 1520, 6720, 28672, 134400, 580608, 2703360, 12021504,
55351296, 250984448, 1151101952
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 11, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 5, 6, 7},
never show up!
Theorem Number, 42, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 24, 198, 880, 5380, 28560, 164934, 924000, 5303340, 30299280, 174574620,
1006825248, 5829520840, 33815445664
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 21, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 43, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 36, 312, 1680, 11280, 70560, 458080, 2975616, 19418112, 127670400,
840390144, 5560828416, 36850418176, 244984836096
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 13, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 5, 6, 7},
never show up!
Theorem Number, 44, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 48, 438, 2720, 19340, 137760, 964390, 7017024, 50038884, 364980000,
2642109756, 19317355200, 141107646680, 1035194608448
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 5, 7},
never show up!
Theorem Number, 45, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 27, 216, 1080, 5535, 34020, 172368, 1041012, 5633712, 32717520,
184926159, 1058315544, 6083437932, 34854046227
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 107, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 46, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 39, 366, 1950, 13355, 84630, 555086, 3660384, 24151554, 160995120,
1072726611, 7191385344, 48262029816, 324988783119
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 629, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 47, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 16, 51, 528, 3060, 23935, 164220, 1219680, 8809332, 65106216, 479262300,
3556725711, 26425456200, 197088262800, 1472727467211
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 127, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 48, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 63, 702, 4410, 37395, 277830, 2235870, 17495352, 140056938, 1117046700,
8979363459, 72278197992, 583933176684, 4727043624303
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 613, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 49, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 13, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 5, 6, 7},
never show up!
Theorem Number, 50, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 3, 19, 67, 291, 1341, 5853, 26419, 120403, 547993, 2513193, 11570989,
53408941, 247299027, 1147809939
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 51, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 37, 145, 881, 4901, 26405, 152097, 857953, 4884805, 28079525, 161316145,
931359313, 5392226789, 31279571237
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 32, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 6, 7},
never show up!
Theorem Number, 52, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 55, 235, 1771, 10801, 67537, 450115, 2882467, 18952597, 124876357,
822501109, 5456962837, 36235266991, 241267084975
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 53, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 16, 61, 231, 896, 3515, 13917, 55501, 222595, 896930, 3628120, 14724022,
59922175, 244456581
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 389, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 54, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 34, 175, 951, 5176, 28687, 160231, 901663, 5103097, 29016472, 165634624,
948599692, 5447994839, 31365144909
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 590, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 55, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 52, 301, 1971, 12396, 80739, 527437, 3472261, 23001919, 153016194,
1022072536, 6848799010, 46022234519, 310008304797
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 431, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 56, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 70, 439, 3291, 22676, 165551, 1202055, 8807551, 64986901, 481075376,
3577692856, 26685660496, 199616797615, 1496806789125
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 590, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 57, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 37, 193, 1001, 5241, 28029, 150529, 815761, 4443049, 24314709, 133573441,
736168057, 4068611353, 22540316717
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 27, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 6, 7},
never show up!
Theorem Number, 58, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 55, 355, 2211, 14261, 92681, 608819, 4026691, 26789041, 179056901,
1201500301, 8088847261, 54610234459, 369590414295
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 49, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 59, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 73, 529, 3721, 26941, 197233, 1456673, 10840465, 81117613, 609893593,
4603215409, 34857719833, 264699597917, 2014944995713
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 32, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 6, 7},
never show up!
Theorem Number, 60, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 91, 715, 5531, 43401, 347565, 2794051, 22682899, 184983085, 1516274145,
12474913045, 102976097173, 852405168343, 7073074138691
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 50, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 61, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 64, 397, 2551, 15976, 104203, 676957, 4447981, 29366443, 194743858,
1296733384, 8661154438, 58014153679, 389517227749
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 388, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 62, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 82, 607, 4311, 31536, 233535, 1743463, 13120255, 99267985, 754699320,
5759824720, 44104291180, 338667328455, 2606900765757
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 590, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 63, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 100, 829, 6371, 51476, 416627, 3415245, 28165861, 233706727, 1948038962,
16301553544, 136861333714, 1152270624935, 9724867347485
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 431, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 64, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 118, 1063, 8731, 75916, 659359, 5805703, 51411295, 458084269, 4100076784,
36841864456, 332129714320, 3002567395231, 27210163458133
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 590, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 65, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 14, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 6, 7},
never show up!
Theorem Number, 66, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 32, 166, 852, 4524, 24432, 132934, 728348, 4014676, 22233312, 123605596,
689449256, 3856481880, 21624138912
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 67, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 56, 328, 2032, 13184, 85696, 562272, 3721664, 24763648, 165534976,
1110924544, 7479881216, 50503294976, 341822273536
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 4, 5, 6, 7},
never show up!
Theorem Number, 68, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 80, 502, 3572, 26164, 190640, 1411750, 10529756, 78907660, 594342080,
4493839420, 34087429352, 259297309288, 1977203630240
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 22, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 69, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 35, 160, 752, 3599, 17446, 85376, 420884, 2087008, 10398016, 52010479,
261021854, 1313707256, 6628095035
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 134, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 70, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 59, 358, 2242, 14299, 92360, 602270, 3956252, 26140330, 173541260,
1156667395, 7734994958, 51873729652, 348741401119
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 590, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 71, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 83, 568, 4092, 29919, 221454, 1655056, 12458036, 94317592, 717428604,
5478493519, 41973619118, 322490785244, 2483811265323
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 171, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 72, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 107, 790, 6302, 50579, 411448, 3380654, 27966932, 232713394, 1945471288,
16327320211, 137477812214, 1160835229064, 9825733252727
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 627, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 73, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 68, 400, 2432, 15024, 93984, 593408, 3773696, 24136192, 155096064,
1000509184, 6475410944, 42027531264, 273436525568
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 6, 7},
never show up!
Theorem Number, 74, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 92, 646, 4652, 34124, 253528, 1901638, 14368844, 109208164, 833981128,
6394017436, 49185717752, 379438594136, 2934361958192
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 19, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 75, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 116, 904, 7232, 58864, 485312, 4038752, 33856064, 285456256, 2418204032,
20565984256, 175486400000, 1501643090432, 12881109687296
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 14, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 6, 7},
never show up!
Theorem Number, 76, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 140, 1174, 10172, 89364, 796056, 7155110, 64782572, 589921948,
5397220776, 49572508924, 456817283288, 4221516171240, 39106924773680
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 22, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 77, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 107, 736, 5312, 38719, 286022, 2132512, 16011188, 120903136, 917200352,
6985016911, 53368875614, 408904516960, 3140554335587
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 134, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 78, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 131, 1030, 8322, 68379, 569256, 4783678, 40494812, 344797498, 2949775116,
25335206659, 218324891150, 1886757094044, 16345408354311
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 590, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 79, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 20, 155, 1336, 11692, 104399, 943630, 8610480, 79141844, 731648920,
6795953980, 63372712495, 592914790574, 5563039388612, 52323374287315
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 171, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 80, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 179, 1654, 15422, 146899, 1415864, 13776718, 135021140, 1330957762,
13181632664, 131060482579, 1307396822006, 13078832786608, 131156898478559
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 627, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 81, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 27, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 5, 6, 7},
never show up!
Theorem Number, 82, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 57, 339, 2073, 12869, 81063, 516371, 3315513, 21415761, 138994683,
905707581, 5921485911, 38825170731, 255192103017
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 51, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 83, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 87, 609, 4323, 31549, 234279, 1757121, 13276995, 100922733, 770828919,
5910673569, 45473210019, 350836300317, 2713419535047
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 54, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 84, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 117, 891, 6993, 56889, 469395, 3909411, 32816745, 277120845, 2351230335,
20027470725, 171156328047, 1466848379655, 12601932138477
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 52, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 85, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 66, 357, 1993, 11344, 65439, 381229, 2237799, 13214763, 78417144,
467210544, 2793104694, 16746295159, 100655033791
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 391, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 86, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 96, 663, 4733, 34464, 254355, 1895735, 14235693, 107538705, 816302490,
6221251320, 47574051372, 364849702967, 2805038513231
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 498, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 87, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 126, 981, 7893, 64844, 539871, 4538333, 38433663, 327393927, 2802193056,
24079196304, 207602903394, 1794990074783, 15558234035031
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 429, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 88, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 156, 1311, 11473, 102604, 929547, 8503063, 78356685, 726274989,
6763643802, 63236216976, 593184569760, 5580127723231, 52621419169831
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 529, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 89, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 111, 753, 5243, 37169, 266871, 1934305, 14122803, 103715217, 765283071,
5669058129, 42134877099, 314054824625, 2346580226951
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 38, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 5, 6},
never show up!
Theorem Number, 90, : Let A(n) be the constant term, in x, of
/ 1 2\n
|3 + ---- + 2/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 141, 1107, 8953, 73789, 616227, 5196627, 44152809, 377379369, 3241135527,
27948336381, 241813226151, 2098240353907, 18252025766941
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 45, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 91, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 171, 1473, 13083, 118389, 1085283, 10044673, 93656115, 878386581,
8277708123, 78317021121, 743453353035, 7077691236469, 67546304093331
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 43, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 92, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 201, 1851, 17633, 171089, 1681599, 16685923, 166785177, 1676848293,
16939092459, 171789670149, 1748022315471, 17837360202671, 182465597624561
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 50, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 93, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 2/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 162, 1269, 10233, 84024, 698463, 5860269, 49524615, 420938451,
3594605688, 30815984736, 265051212390, 2286157926087, 19766997379647
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 391, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 94, : Let A(n) be the constant term, in x, of
/ 1 2\n
|3 + ---- + 2/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 192, 1671, 14973, 136664, 1263699, 11798327, 110974989, 1050011433,
9982721994, 95287086024, 912593172780, 8765282582247, 84397758645087
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 499, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 95, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 222, 2085, 20133, 198004, 1972575, 19840221, 201031647, 2048944815,
20983122240, 215740158720, 2225578627314, 23024747205807, 238791366352887
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 429, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 96, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 2/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 252, 2511, 25713, 268164, 2832651, 30206871, 324489645, 3506130117,
38064293226, 414877585824, 4536977899392, 49756312005903, 547012699861527
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 529, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 97, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 40, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 4, 5, 6, 7},
never show up!
Theorem Number, 98, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 2, 27, 6, 270, 1235, 1890, 22750, 72576, 255402, 1746360, 5493939, 26594568,
135246540, 485431947
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 647, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 99, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 54, 24, 1080, 5020, 15120, 182560, 671328, 4090464, 28939680, 123872496,
861404544, 4873083072, 25497055584
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 77, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 5, 7},
never show up!
Theorem Number, 100, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 81, 54, 2430, 11475, 51030, 618030, 2571912, 20728386, 151559100,
809349651, 6620101488, 41146707888, 270064675881
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 599, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 101, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 3, 54, 60, 555, 945, 6174, 13692, 72576, 191070, 887931, 2617758,
11184459, 35543508
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 283, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 102, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 30, 132, 900, 3950, 24150, 126308, 701400, 3925908, 21624900, 121975854,
681415020, 3840592470, 21661690050
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 96, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 103, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 57, 222, 2280, 10975, 81795, 530670, 3381924, 23536800, 152618070,
1039404795, 6982162902, 47006723907, 319562335092
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 302, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 104, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 84, 324, 4200, 21750, 185220, 1378020, 9654960, 77517972, 560138040,
4319736894, 32810561784, 248190577206, 1910801416524
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 96, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 105, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 12, 216, 480, 4560, 15120, 106848, 440832, 2685312, 12481920, 70608384,
349899264, 1910168832, 9793335552
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 61, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 5, 6, 7},
never show up!
Theorem Number, 106, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 39, 366, 1950, 13355, 84630, 555086, 3660384, 24151554, 160995120,
1072726611, 7191385344, 48262029816, 324988783119
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 629, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 107, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 16, 66, 528, 3960, 26860, 212520, 1525440, 11760672, 88202016, 674018400,
5147940336, 39453860160, 303552300480, 2338399199136
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 77, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 6, 7},
never show up!
Theorem Number, 108, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 93, 702, 6510, 45195, 410130, 3196830, 27180552, 225560538, 1888355700,
15956447859, 134330645592, 1140101509404, 9668650244253
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 613, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 109, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 27, 486, 1620, 15795, 76545, 581742, 3367980, 23147208, 145063710,
961967259, 6231677166, 40944989943, 268823406852
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 285, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 110, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 20, 54, 708, 3780, 33230, 224910, 1780324, 13086360, 101075940, 765885780,
5900921070, 45300140028, 350025900510, 2705769780714
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 81, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 111, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 22, 81, 942, 6480, 56455, 456435, 3829630, 32176116, 271455912, 2307734550,
19643430939, 168054990246, 1440139057071, 12379261890996
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 304, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 112, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 24, 108, 1188, 9720, 85590, 782460, 6928740, 63930384, 579843684, 5355088200,
49289858046, 456764485320, 4238037731070, 39439963911348
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 118, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 113, : Let A(n) be the constant term, in x, of
/ 1 \n
|1 + ---- + 3/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 57, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 5, 6, 7},
never show up!
Theorem Number, 114, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 3, 34, 127, 591, 3516, 17403, 89559, 486223, 2563693, 13626768, 73395664,
394170076, 2123218527, 11485869489
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 588, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 115, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 67, 265, 1781, 13001, 75755, 509377, 3424153, 22171405, 148805075,
996671545, 6649852093, 44795141249, 301849584587
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 178, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 116, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 100, 415, 3571, 28576, 187237, 1492135, 11255167, 83425897, 646296982,
4920865984, 37636345072, 290615028991, 2236998217825
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 515, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 117, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 22, 103, 421, 1876, 8212, 36751, 164731, 744367, 3375802, 15375724,
70247932, 321870472, 1478312752
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 101, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 118, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 55, 301, 1941, 12051, 76539, 491653, 3172213, 20609749, 134486859,
880976911, 5790193891, 38161698927, 252127029345
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 218, states .
For example, A(100000), mudolo , 8, equals , 5
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 119, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 88, 511, 4061, 29276, 216476, 1639023, 12344875, 93984811, 718288616,
5507806756, 42393510940, 327138855824, 2530654004708
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 98, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 120, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 121, 733, 6781, 53671, 440203, 3731701, 31129573, 264009433, 2244464773,
19134087919, 163865679199, 1406297414731, 12100128720511
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 304, states .
For example, A(100000), mudolo , 8, equals , 5
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 121, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 49, 337, 1801, 11101, 65353, 398497, 2418961, 14842093, 91288033,
564173809, 3496652953, 21735716029, 135429712249
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 114, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 6, 7},
never show up!
Theorem Number, 122, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 82, 607, 4311, 31536, 233535, 1743463, 13120255, 99267985, 754699320,
5759824720, 44104291180, 338667328455, 2606900765757
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 590, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 123, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 115, 889, 7421, 60101, 504827, 4240545, 35968201, 306713977, 2627331587,
22596482569, 194964688309, 1686946101725, 14631750660635
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 178, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 124, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 148, 1183, 11131, 96916, 891409, 8162743, 75430255, 701729869,
6551407534, 61437972256, 577905187120, 5451487479751, 51549534477733
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 529, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 125, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 82, 703, 4501, 33616, 239464, 1763119, 12954331, 96022099, 714380734,
5336114356, 39990027052, 300504579688, 2263719904192
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 100, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 126, : Let A(n) be the constant term, in x, of
/ 1 2\n
|1 + ---- + 3/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 21, 115, 1045, 8061, 67911, 563991, 4774869, 40568101, 347130241, 2982786951,
25735012711, 222755304331, 1933596302379, 16825136788845
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 214, states .
For example, A(100000), mudolo , 8, equals , 5
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 127, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 23, 148, 1399, 12221, 111416, 1023968, 9495823, 88759435, 834019663,
7875349868, 74646026764, 709883092348, 6769870809872, 64719048195188
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 99, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 128, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 181, 1765, 16981, 164251, 1631575, 16219141, 163031509, 1645522885,
16695438145, 170022115495, 1737195291703, 17799551994823, 182818704607291
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 284, states .
For example, A(100000), mudolo , 8, equals , 5
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 129, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 68, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 6, 7},
never show up!
Theorem Number, 130, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 47, 286, 1602, 9699, 60132, 371214, 2307548, 14462626, 91035012,
574991971, 3644088086, 23160978000, 147557748987
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 585, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 131, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 86, 568, 3832, 29084, 215896, 1601632, 12091424, 91668448, 696993376,
5324668144, 40813043936, 313636507136, 2416170403936
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 81, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 132, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 125, 862, 6722, 58339, 480440, 4024990, 34336196, 292592410, 2506012280,
21575034595, 186221653022, 1611833827348, 13987050486065
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 643, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 133, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 47, 238, 1232, 6499, 34715, 187198, 1016840, 5555560, 30497150,
168073195, 929348396, 5153362231, 28646281502
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 254, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 134, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 86, 580, 4092, 29454, 214314, 1574500, 11652224, 86731012, 648619644,
4869770734, 36682896824, 277107171150, 2098432827606
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 88, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 135, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 125, 934, 7612, 63239, 527893, 4458990, 37932272, 324456424, 2788550998,
24059445931, 208264503332, 1807870237775, 15731693608750
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 294, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 136, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 164, 1300, 11792, 107974, 988472, 9194308, 86027960, 809204836,
7649884112, 72591979486, 691100890820, 6598091552446, 63145950761744
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 134, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 137, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 92, 616, 4112, 28144, 194672, 1359712, 9564608, 67668736, 480993152,
3432257536, 24572409344, 176415489280, 1269645293312
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 66, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 6, 7},
never show up!
Theorem Number, 138, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 131, 1030, 8322, 68379, 569256, 4783678, 40494812, 344797498, 2949775116,
25335206659, 218324891150, 1886757094044, 16345408354311
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 590, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 139, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 20, 170, 1456, 13192, 120524, 1116880, 10446720, 98412704, 932492320,
8877227680, 84841358320, 813525505184, 7822772575232, 75406885390240
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 74, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 6, 7},
never show up!
Theorem Number, 140, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 209, 1894, 18722, 184699, 1850564, 18722638, 190691300, 1953749362,
20110451264, 207809229379, 2154452620166, 22399057482208, 233442446848109
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 631, states .
For example, A(100000), mudolo , 8, equals , 2
all the congruences classes mod, 8, show up
Theorem Number, 141, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 143, 1150, 9032, 73099, 597179, 4926478, 40930136, 341993392, 2870906414,
24193487179, 204549937724, 1734265825699, 14739563348918
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 249, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 142, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 24, 182, 1636, 14652, 134574, 1249698, 11719908, 110707904, 1051886164,
10041899628, 96243953326, 925494049352, 8924981592726, 86279519856942
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 99, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 143, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 26, 221, 2134, 20932, 209039, 2115157, 21598462, 222173024, 2298591856,
23893662982, 249347367691, 2610737565620, 27412590681467, 288535722978646
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 294, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 144, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 28, 260, 2644, 27872, 296614, 3206576, 34956100, 383915672, 4240653748,
47061843776, 524325629854, 5860892884628, 65697830284870, 738240048624680
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 114, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 145, : Let A(n) be the constant term, in x, of
/ 1 \n
|3 + ---- + 3/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 111, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 5, 6, 7},
never show up!
Theorem Number, 146, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 72, 519, 3573, 24644, 173463, 1236391, 8870013, 63965061, 463456458,
3371364456, 24605785116, 180089790591, 1321295828067
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 515, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 147, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 117, 969, 7623, 62449, 523029, 4402561, 37283355, 317766933, 2721298869,
23392826169, 201748806639, 1744882927017, 15127859195397
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 230, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 148, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 162, 1431, 12393, 114264, 1064745, 9946071, 93723885, 888873345,
8466051960, 80944806600, 776511880992, 7470005128335, 72034992484227
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 560, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 149, : Let A(n) be the constant term, in x, of
/ 1 \n
|3 + ---- + 3/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 84, 495, 3003, 18564, 116280, 735471, 4686825, 30045015, 193536720,
1251677700, 8122425444, 52860229080, 344867425584
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 73, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 150, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 129, 1005, 7983, 64619, 530001, 4388645, 36608511, 307172637, 2589753741,
21920819919, 186169052241, 1585620914055, 13538300225319
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 216, states .
For example, A(100000), mudolo , 8, equals , 5
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 151, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 174, 1527, 13683, 125644, 1167792, 10951887, 103467225, 983191059,
9386847462, 89971525356, 865223993988, 8344144919808, 80667564994164
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 119, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 152, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 219, 2061, 20103, 201759, 2043513, 20886357, 215095503, 2227784481,
23181720543, 242168099391, 2538160889085, 26677526149491, 281081075987229
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 304, states .
For example, A(100000), mudolo , 8, equals , 5
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 153, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 147, 1089, 8283, 64149, 503163, 3984129, 31778355, 254950101, 2055118563,
16631351361, 135039238155, 1099575642837, 8975450076747
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 166, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 154, : Let A(n) be the constant term, in x, of
/ 1 2\n
|3 + ---- + 3/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 192, 1671, 14973, 136664, 1263699, 11798327, 110974989, 1050011433,
9982721994, 95287086024, 912593172780, 8765282582247, 84397758645087
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 499, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 155, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 237, 2265, 22383, 225229, 2294925, 23607201, 244625547, 2549708865,
26701907565, 280741645545, 2961531192519, 31330045673637, 332256772573437
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 230, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 156, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 282, 2871, 30513, 329964, 3610701, 39892071, 443946045, 4969177317,
55884278376, 630954015624, 7147318455072, 81192874716183, 924604690710327
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 590, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 157, : Let A(n) be the constant term, in x, of
/ 1 \n
|---- + 3/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 216, 1863, 16443, 147744, 1344276, 12345615, 114202953, 1062534267,
9932277996, 93207429324, 877574192004, 8285942274840, 78425918957376
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 81, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 158, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 29, 261, 2517, 24903, 251039, 2563557, 26431477, 274548879, 2868644169,
30117280977, 317454892071, 3357408221001, 35609843787267, 378626397171291
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 216, states .
For example, A(100000), mudolo , 8, equals , 5
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 159, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 31, 306, 3183, 34083, 371464, 4100988, 45707503, 513189945, 5795720631,
65766426498, 749233731156, 8564024112660, 98169292496544, 1128088286442756
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 115, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 160, : Let A(n) be the constant term, in x, of
/ 1 2\n
|---- + 3/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 33, 351, 3861, 43983, 509139, 5970429, 70675173, 842740767, 10107524493,
121801153059, 1473552741879, 17886314377701, 217724895110511,
2656812164068161
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 284, states .
For example, A(100000), mudolo , 8, equals , 5
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 161, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 4, 5, 6, 7},
never show up!
Theorem Number, 162, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 3, 24, 60, 175, 840, 1680, 10164, 20664, 115500, 281391, 1297296, 3838692,
14897883
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 127, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 163, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 6, 96, 240, 1340, 6720, 22400, 161952, 459648, 3622080, 10888944,
78414336, 272638080, 1691385696
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 15, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 5, 7},
never show up!
Theorem Number, 164, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 9, 216, 540, 4455, 22680, 105840, 818748, 2980152, 27318060, 97037919,
875674800, 3421386540, 27672053409
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 125, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 165, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 2, 6, 6, 40, 80, 210, 742, 1680, 5292, 15180, 40524, 123552, 343772, 986986
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 21, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 166, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 9, 78, 240, 1335, 5355, 26110, 115668, 543816, 2499750, 11680251,
54478710, 255144175, 1198160964
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 304, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 167, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 12, 198, 560, 5020, 20580, 144774, 708960, 4486860, 23980440, 144874620,
809018496, 4792044400, 27372997652
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 18, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 168, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 15, 366, 1000, 12095, 50925, 454174, 2386860, 18396504, 108650850,
779959851, 4901037570, 34002807839, 220881360700
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 304, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 169, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 24, 24, 320, 1120, 3360, 22624, 75264, 330624, 1647360, 6141696, 28993536,
128567296, 531474944
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 5, 6, 7},
never show up!
Theorem Number, 170, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 27, 144, 900, 4175, 26460, 136640, 805140, 4489128, 25678620, 147274479,
842037768, 4863568424, 27995674707
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 127, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 171, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 30, 312, 1600, 11100, 71400, 458528, 3108000, 20083392, 136646400,
899829744, 6102233280, 40770878720, 276156680800
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 5, 7},
never show up!
Theorem Number, 172, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 16, 33, 528, 2420, 22855, 143220, 1139488, 8072988, 60993576, 452043900,
3381052191, 25456211352, 190893946672, 1445604273113
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 127, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 173, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 54, 54, 1080, 5400, 17010, 168966, 734832, 3735396, 26462700, 121920876,
720555264, 4342096044, 22027599594
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 21, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 174, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 57, 222, 2280, 10975, 81795, 530670, 3381924, 23536800, 152618070,
1039404795, 6982162902, 47006723907, 319562335092
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 302, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 175, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 60, 438, 3600, 21860, 186900, 1255142, 9935520, 72688644, 553179000,
4194002076, 31747510080, 243010832064, 1850355807300
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 17, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 5, 7},
never show up!
Theorem Number, 176, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 63, 702, 5040, 39015, 337365, 2547342, 22210524, 174808368, 1491453810,
12159698859, 102397032738, 851248720179, 7145398368108
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 302, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 177, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 28, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 5, 6, 7},
never show up!
Theorem Number, 178, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 16, 61, 251, 1016, 4355, 18621, 81205, 356155, 1573430, 6986200, 31140994,
139281455, 624616361
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 425, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 179, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 31, 169, 861, 4461, 24879, 134401, 761161, 4256689, 24262239, 138207961,
792787477, 4559039109, 26298912831
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 61, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 6},
never show up!
Theorem Number, 180, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 46, 325, 1831, 11296, 73333, 458221, 3058453, 19770643, 132459988,
876676384, 5889337390, 39487679167, 266278586041
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 425, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 181, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 3, 13, 43, 151, 561, 2073, 7715, 29011, 109633, 416043, 1585189, 6059353,
23224995, 89233693
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 76, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 182, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 28, 151, 781, 4216, 22912, 125903, 696619, 3876607, 21673972, 121646284,
684987772, 3867943184, 21894249748
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 99, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 183, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 43, 307, 1771, 11741, 75041, 496147, 3271363, 21799681, 145653641,
977889661, 6584131477, 44463245243, 300965380363
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 70, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 184, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 58, 511, 3121, 24096, 170220, 1283087, 9497587, 71685175, 540207570,
4100350420, 31177505308, 237913339392, 1819227859828
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 115, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 185, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 37, 145, 721, 3941, 19685, 101921, 539425, 2828485, 14942885, 79455025,
422942833, 2258151845, 12090801637
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 44, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 6, 7},
never show up!
Theorem Number, 186, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 52, 301, 1971, 12396, 80739, 527437, 3472261, 23001919, 153016194,
1022072536, 6848799010, 46022234519, 310008304797
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 431, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 187, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 67, 505, 3581, 26161, 194923, 1453985, 10981417, 83169013, 633698803,
4844056009, 37158496597, 285810497545, 2203736079467
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 61, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 188, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 82, 757, 5551, 46196, 373997, 3099965, 25778917, 215711767, 1814123312,
15307993504, 129640671694, 1100704760039, 9369279969157
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 429, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 189, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 73, 307, 1951, 13861, 81397, 523699, 3469123, 22152637, 144481327,
950666509, 6220704673, 40951593151, 270535280113
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 74, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 190, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 88, 511, 4061, 29276, 216476, 1639023, 12344875, 93984811, 718288616,
5507806756, 42393510940, 327138855824, 2530654004708
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 98, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 191, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 103, 763, 6531, 51441, 433245, 3598435, 30310771, 256550845, 2179900845,
18608015845, 159288912589, 1367623508343, 11769778788783
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 74, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 192, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 118, 1063, 9361, 81316, 743464, 6674095, 61288435, 561646819, 5188163014,
48049343596, 446613538060, 4162613091040, 38889202725028
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 119, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 193, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 2|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 13, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 6, 7},
never show up!
Theorem Number, 194, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 35, 160, 772, 3839, 19546, 101280, 531764, 2820328, 15075436, 81076879,
438164534, 2377297784, 12939840475
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 152, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 195, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 62, 352, 2112, 12924, 81384, 520384, 3373856, 22095232, 145856064,
968879344, 6468148832, 43355525568, 291572336352
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 18, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 196, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 89, 592, 4052, 28279, 204122, 1489408, 11047292, 82683016, 624138572,
4740876991, 36196764086, 277510473088, 2134831686929
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 152, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 197, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 2 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 6, 26, 118, 532, 2424, 11202, 52294, 245852, 1162276, 5520132, 26318956,
125894264, 603888172, 2903740306
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 198, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 53, 310, 1892, 11839, 75245, 483326, 3128768, 20375440, 133329110,
875909995, 5773461956, 38163131387, 252880464038
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 294, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 199, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 80, 550, 3852, 28004, 206908, 1548614, 11690252, 88826884, 678354448,
5201650876, 40021385432, 308804317696, 2388582610260
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 200, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 107, 838, 6412, 51879, 424671, 3533758, 29660408, 250787968, 2131747026,
18198477499, 155900165072, 1339453334587, 11536897514542
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 294, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 201, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 2 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 8, 56, 328, 1872, 11264, 68896, 422496, 2608832, 16215808, 101245696,
634457344, 3988795904, 25147276288, 158919553536
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 4, 5, 6, 7},
never show up!
Theorem Number, 202, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 12, 83, 568, 4092, 29919, 221454, 1655056, 12458036, 94317592, 717428604,
5478493519, 41973619118, 322490785244, 2483811265323
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 171, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 203, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 16, 110, 856, 6912, 56764, 473552, 3985888, 33802976, 288314176, 2470687232,
21254884336, 183453431072, 1587863444288, 13777051707360
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 17, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 204, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 20, 137, 1192, 10332, 92759, 843670, 7754352, 71825276, 669148600,
6263877820, 58863975295, 554990112926, 5247322710244, 49732947077217
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 169, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 205, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 2 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 10, 98, 646, 4292, 31744, 232850, 1698022, 12567932, 93653980, 699652340,
5247942220, 39505205144, 298161175420, 2255610249458
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 206, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 14, 125, 934, 7612, 63239, 527893, 4458990, 37932272, 324456424, 2788550998,
24059445931, 208264503332, 1807870237775, 15731693608750
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 294, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 207, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 18, 152, 1270, 11532, 104364, 961116, 8930086, 83542796, 786199228,
7432817856, 70545012124, 671743016024, 6414432545616, 61400028720612
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 20, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 208, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 2 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
2, 22, 179, 1654, 16052, 156079, 1550999, 15504430, 156274568, 1583754712,
16125974834, 164835049339, 1690401666800, 17383950058063, 179208657048374
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 294, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 209, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 40, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 5, 6, 7},
never show up!
Theorem Number, 210, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 66, 357, 2013, 11704, 69639, 421773, 2590095, 16080003, 100696764,
634971984, 4026467682, 25649269239, 164004740211
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 425, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 211, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 105, 681, 4623, 32309, 230961, 1680065, 12388875, 92345337, 694259481,
5255535129, 40006451943, 305926461837, 2348176521105
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 72, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 212, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 144, 1053, 8073, 63504, 511353, 4187997, 34769007, 291769371, 2469513258,
21046597416, 180378463086, 1553020693623, 13421838407859
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 425, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 213, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 11, 51, 267, 1453, 8009, 44523, 249475, 1407705, 7989561, 45561453,
260841381, 1498267683, 8630351531, 49834369891
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 70, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 214, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 90, 591, 4083, 29064, 210780, 1547695, 11464281, 85477095, 640576170,
4820411220, 36398556756, 275640152992, 2092580941860
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 115, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 215, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 129, 963, 7553, 61189, 506187, 4247091, 35990697, 307223289, 2637127947,
22735986381, 196719062751, 1707147542707, 14852303960369
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 70, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 216, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 168, 1383, 11863, 105344, 955944, 8807983, 82033377, 770071743,
7272174264, 68995741164, 657063780948, 6276730763312, 60115676023108
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 97, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 217, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 87, 609, 4163, 28669, 200679, 1420225, 10119939, 72497133, 521739639,
3769359009, 27320908995, 198577505629, 1446808589447
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 66, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 218, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 126, 981, 7893, 64844, 539871, 4538333, 38433663, 327393927, 2802193056,
24079196304, 207602903394, 1794990074783, 15558234035031
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 429, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 219, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 165, 1401, 12463, 113529, 1050213, 9817313, 92480619, 876391101,
8344970373, 79774962441, 765156914343, 7359792205073, 70965068021365
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 72, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 220, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 204, 1869, 17873, 175684, 1756905, 17771245, 181242591, 1859938335,
19180826910, 198596982120, 2063136787182, 21493951800031, 224474815572719
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 431, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 221, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 1/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 15, 135, 1107, 8613, 69309, 571455, 4741011, 39530025, 331582005, 2794975065,
23647888845, 200717858331, 1708381779399, 14575656833055
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 72, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 222, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 19, 174, 1527, 13683, 125644, 1167792, 10951887, 103467225, 983191059,
9386847462, 89971525356, 865223993988, 8344144919808, 80667564994164
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 119, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 223, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 23, 213, 1995, 19593, 195929, 1983999, 20284931, 208906809, 2163923253,
22520484759, 235295215989, 2466511223751, 25928668096431, 273236607114813
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 74, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 224, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 1/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 27, 252, 2511, 26343, 281124, 3045276, 33307983, 367007841, 4067511147,
45292539636, 506315837124, 5678678950740, 63870003270576, 720120739050612
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 99, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 225, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 5, 6, 7},
never show up!
Theorem Number, 226, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 25, 97, 521, 2501, 12545, 64065, 325393, 1674565, 8636585, 44720545,
232429081, 1210941317, 6325164305
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 32, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 6, 7},
never show up!
Theorem Number, 227, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 49, 241, 1761, 10041, 67089, 429409, 2785729, 18358249, 120259569,
796268881, 5272973473, 35045465625, 233510713809
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 5, 6, 7},
never show up!
Theorem Number, 228, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 73, 433, 3721, 23581, 190513, 1378273, 10517905, 80210413, 609407833,
4698123409, 36048870937, 278629449853, 2154641061313
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 32, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 6, 7},
never show up!
Theorem Number, 229, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 19, 73, 301, 1241, 5195, 21953, 93385, 399565, 1717475, 7410745, 32080933,
139264529, 606012139
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 53, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 230, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 43, 265, 1581, 9741, 60579, 380353, 2405545, 15299089, 97761819,
627109561, 4035938245, 26047182149, 168512126883
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 178, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 231, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 67, 505, 3581, 26161, 194923, 1453985, 10981417, 83169013, 633698803,
4844056009, 37158496597, 285810497545, 2203736079467
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 61, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 232, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 91, 793, 6301, 51461, 435107, 3632609, 31014217, 263924857, 2266951787,
19502967529, 168496623829, 1459244026397, 12669561636931
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 178, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 233, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 49, 241, 1441, 8121, 46929, 275297, 1616449, 9568489, 56878449, 339316561,
2031216097, 12191914905, 73355518609
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 5, 6, 7},
never show up!
Theorem Number, 234, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 73, 529, 3721, 26941, 197233, 1456673, 10840465, 81117613, 609893593,
4603215409, 34857719833, 264699597917, 2014944995713
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 32, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 6, 7},
never show up!
Theorem Number, 235, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 97, 865, 6721, 56561, 470177, 3982273, 33843841, 289684177, 2489672417,
21484861729, 185996101825, 1614743032241, 14052331289377
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 8, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 5, 6, 7},
never show up!
Theorem Number, 236, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 21, 121, 1249, 10441, 97941, 892641, 8349377, 78118033, 737035861,
6978684681, 66360270241, 632981525593, 6054915252309, 58058495769841
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 32, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 6, 7},
never show up!
Theorem Number, 237, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 91, 505, 3901, 26641, 187363, 1358113, 9730153, 70618933, 514644043,
3759227209, 27578274517, 202798937641, 1494850486051
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 53, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 238, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 115, 889, 7421, 60101, 504827, 4240545, 35968201, 306713977, 2627331587,
22596482569, 194964688309, 1686946101725, 14631750660635
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 178, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 239, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 21, 139, 1321, 11661, 107241, 995331, 9311233, 87855817, 832941661,
7937381211, 75914930521, 728509774981, 7010399216289, 67625067981219
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 61, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 240, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 1 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 163, 1801, 16621, 169021, 1685755, 17174977, 175424617, 1805017825,
18647693395, 193433769145, 2012924810053, 21005971610677, 219738531772603
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 178, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 241, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 3|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323,
4782969, 14348907
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 5, 6, 7},
never show up!
Theorem Number, 242, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 75, 465, 3003, 20029, 136419, 941985, 6567411, 46113453, 325553979,
2308301169, 16424559531, 117213313629, 838596904275
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 43, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 243, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 123, 897, 6963, 55889, 457131, 3791489, 31753059, 267811857, 2271082971,
19342185729, 165311886483, 1417029334353, 12177024531723
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 5, 6, 7},
never show up!
Theorem Number, 244, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 171, 1377, 12123, 109269, 1004643, 9374913, 88309683, 837885141,
7993601883, 76590962721, 736454791179, 7102209714453, 68664009249171
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 43, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 245, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 3 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 13, 69, 393, 2303, 13729, 82869, 504961, 3099723, 19139733, 118747269,
739662009, 4622692311, 28973271193, 182042465189
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 62, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 246, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 117, 873, 6783, 53909, 434661, 3540161, 29052459, 239840217, 1989519381,
16569202329, 138455300727, 1160272014989, 9747281151477
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 230, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 247, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 165, 1401, 12463, 113529, 1050213, 9817313, 92480619, 876391101,
8344970373, 79774962441, 765156914343, 7359792205073, 70965068021365
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 72, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 248, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 213, 1977, 19343, 193549, 1969845, 20263777, 210108939, 2191759425,
22973774805, 241762494345, 2552615050599, 27027715134949, 286875624839333
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 230, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 249, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 3 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 17, 123, 897, 6643, 50129, 383211, 2956417, 22971363, 179511057, 1409365851,
11108173569, 87838769619, 696545218001, 5536916176843
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 5, 6, 7},
never show up!
Theorem Number, 250, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 171, 1473, 13083, 118389, 1085283, 10044673, 93656115, 878386581,
8277708123, 78317021121, 743453353035, 7077691236469, 67546304093331
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 43, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 251, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 219, 2097, 20723, 208969, 2135115, 22025313, 228879075, 2392300665,
25123555515, 264882406545, 2801979624915, 29724048024745, 316093568851499
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 5, 6, 7},
never show up!
Theorem Number, 252, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 29, 267, 2769, 29563, 322829, 3573027, 39933217, 449598579, 5091390909,
57928915707, 661687723761, 7583049315819, 87148577826605, 1004007555520147
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 43, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 253, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 2/x + 3 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 21, 189, 1593, 13743, 121689, 1089693, 9840609, 89511723, 818863101,
7525639773, 69429995721, 642636244071, 5964774222897, 55497229084269
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 62, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 254, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 25, 237, 2265, 22383, 225229, 2294925, 23607201, 244625547, 2549708865,
26701907565, 280741645545, 2961531192519, 31330045673637, 332256772573437
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 230, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 255, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 29, 285, 2985, 32223, 353969, 3938637, 44239169, 500533323, 5696099109,
65129071197, 747614001561, 8610311984823, 99446801724201, 1151402024923965
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 72, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 256, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 2/x + 3 + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
3, 33, 333, 3753, 43263, 508869, 6061149, 72878913, 882668907, 10752276393,
131597190189, 1616928532569, 19932804539703, 246417800073597,
3053770977909933
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 230, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 257, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 7, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 4, 5, 6, 7},
never show up!
Theorem Number, 258, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 4, 27, 24, 540, 1375, 7560, 46480, 151956, 1028664, 4365900, 21269391,
115459344, 509303652, 2732997267
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 127, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 259, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 8, 54, 96, 2160, 6140, 60480, 380800, 1941408, 16587648, 85821120, 630549744,
4026806784, 25057718400, 175879607904
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 15, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 5, 7},
never show up!
Theorem Number, 260, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 81, 216, 4860, 15255, 204120, 1315440, 9001692, 84628152, 515300940,
4671075519, 33100507440, 257016808620, 2057492077641
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 125, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 261, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 6, 6, 54, 120, 600, 1890, 7686, 27888, 106596, 405900, 1536876, 5930496,
22580844, 87393306
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 21, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 262, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 10, 33, 222, 1320, 7375, 47355, 275310, 1736196, 10533600, 65706630,
407151195, 2540530278, 15886755027, 99530939508
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 302, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 263, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 14, 60, 438, 3600, 21860, 186900, 1255142, 9935520, 72688644, 553179000,
4194002076, 31747510080, 243010832064, 1850355807300
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 17, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 5, 7},
never show up!
Theorem Number, 264, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 87, 702, 6960, 45015, 465885, 3420942, 31646076, 260992368, 2266338690,
19641326859, 168546711762, 1476712358979, 12765083222892
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 302, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 265, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 12, 24, 216, 960, 5280, 30240, 155232, 913920, 4862592, 28005120, 154623744,
877713408, 4942958592, 27981617664
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 10, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 5, 6, 7},
never show up!
Theorem Number, 266, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 16, 51, 528, 3060, 23935, 164220, 1219680, 8809332, 65106216, 479262300,
3556725711, 26425456200, 197088262800, 1472727467211
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 127, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 267, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 20, 78, 888, 6240, 54620, 447720, 3783584, 32192160, 273792960, 2354626560,
20223463920, 174881513664, 1513047169920, 13140216337248
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 16, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 3, 5, 7},
never show up!
Theorem Number, 268, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 24, 105, 1296, 10500, 98295, 926100, 8481984, 81711420, 763585704,
7355432700, 69944084991, 674045812440, 6476674525464, 62569963481025
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 127, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 269, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 18, 54, 486, 3240, 19440, 153090, 949158, 7103376, 47947788, 342090540,
2413686924, 17023118112, 121627476828, 862150002714
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 21, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 270, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 22, 81, 942, 6480, 56455, 456435, 3829630, 32176116, 271455912, 2307734550,
19643430939, 168054990246, 1440139057071, 12379261890996
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 304, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 271, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 26, 108, 1446, 10800, 109820, 971460, 9359686, 87327072, 835927596,
7957022040, 76432242876, 734600161152, 7089753603504, 68541504539508
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 18, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {3, 5, 7}, never show up!
Theorem Number, 272, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 3 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
0, 30, 135, 1998, 16200, 180495, 1743525, 18335646, 187075980, 1954040760,
20334179250, 213218995275, 2239378803090, 23600482604127, 249264553437900
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 304, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 273, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 1|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 29, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 5, 6, 7},
never show up!
Theorem Number, 274, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 5, 40, 157, 971, 5576, 30395, 179005, 1031413, 5980315, 35100110, 205693720,
1211220466, 7155115007, 42338723705
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 425, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 275, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 9, 79, 361, 3261, 21741, 154239, 1167489, 8350729, 62256049, 461728719,
3426137881, 25657449013, 191916851205, 1441012522959
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 61, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 6},
never show up!
Theorem Number, 276, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 118, 613, 6871, 49456, 423613, 3667693, 30117205, 262818163, 2235089308,
19251393184, 166733675902, 1440502088143, 12526084088713
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 425, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 277, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 1 + x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 7, 25, 115, 511, 2341, 10837, 50611, 238147, 1126717, 5355967, 25557709,
122356417, 587411839, 2826889345
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 74, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 278, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 11, 64, 415, 2861, 19436, 135836, 952239, 6735691, 47899531, 342216656,
2454572836, 17662711132, 127456452176, 921970893764
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 98, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 279, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 15, 103, 763, 6531, 51441, 433245, 3598435, 30310771, 256550845, 2179900845,
18608015845, 159288912589, 1367623508343, 11769778788783
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 74, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 280, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 142, 1159, 11521, 99316, 955144, 8852719, 83961043, 798667459,
7620245854, 73134845356, 703218082828, 6785305011616, 65610936999172
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 119, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 281, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 1 + 2 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 13, 61, 385, 2401, 14941, 96013, 615553, 3993793, 26015533, 170310493,
1119220609, 7378509217, 48780642301, 323266358701
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 44, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 3, 4, 6, 7},
never show up!
Theorem Number, 282, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 2 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 17, 100, 829, 6371, 51476, 416627, 3415245, 28165861, 233706727, 1948038962,
16301553544, 136861333714, 1152270624935, 9724867347485
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 431, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 283, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 2 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 21, 139, 1321, 11661, 107241, 995331, 9311233, 87855817, 832941661,
7937381211, 75914930521, 728509774981, 7010399216289, 67625067981219
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 61, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6, 7},
never show up!
Theorem Number, 284, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 2 x + 3 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 25, 178, 1861, 18271, 183196, 1884205, 19328317, 201141637, 2097094975,
22004853520, 231614306320, 2446540491838, 25912508000887, 275122695839653
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 429, states .
For example, A(100000), mudolo , 8, equals , 0
all the congruences classes mod, 8, show up
Theorem Number, 285, : Let A(n) be the constant term, in x, of
/ 2 \n
|---- + 3/x + 1 + 3 x|
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 19, 109, 811, 6391, 47521, 376489, 2937187, 23264659, 185072689, 1477981099,
11857932901, 95398253497, 769775390515, 6225910981309
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 76, states .
For example, A(100000), mudolo , 8, equals , 1
The congruence classes mod, 8, in the following set , {0, 2, 4, 6},
never show up!
Theorem Number, 286, : Let A(n) be the constant term, in x, of
/ 2 2\n
|---- + 3/x + 1 + 3 x + x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 23, 148, 1399, 12221, 111416, 1023968, 9495823, 88759435, 834019663,
7875349868, 74646026764, 709883092348, 6769870809872, 64719048195188
We are interested in A(n) modulo , 8
Then there is a Congruence Automata to compute it in linear-time (in bit-siz\
e, i.e. log-time in n)
with , 99, states .
For example, A(100000), mudolo , 8, equals , 0
The congruence classes mod, 8, in the following set , {2, 6}, never show up!
Theorem Number, 287, : Let A(n) be the constant term, in x, of
/ 2 2\n
|1 + ---- + 3/x + 3 x + 2 x |
| 2 |
\ x /
For the record, the first 15 terms of the sequence are:
1, 27, 187, 2035, 19371, 198861, 2021937, 2091912