#ATTENDANCE QUIZ FOR LECTURE 7 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p7
#with an attachment called
#p7FirstLast.txt
#(e.g. p7DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Sept. 28, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE:

PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH BY THE ANSWER


Question 1 
Let k be the 3 digit number consisting of your 3rd, 4th and 5th RUID digits. What is g(k)?

Answer 1:
3rd digit=7 , 4th digit= 0, 5th digit=0
k=700
g(700)=g(699)+g(697)+g(696)



Question 2
Is {g(k)} in the OEIS? If yes, what is the A number, if not should it be?

Answer 2:
Was confused about this question, were we supposed to use the alphabet {1,3,4}?



Question 3
For i=3,4,5,... compute 
SeqRec([[1$I],[0$i-1]],30)

Answer 3:

i=3
A000073
[0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136, 5768, 10609, 19513, 35890, 66012, 121415, 223317, 410744, 755476, 1389537, 2555757, 4700770, 8646064, 15902591]

i=4
A000078
[0, 0, 0, 1, 1, 2, 4, 8, 15, 29, 56, 108, 208, 401, 773, 1490, 2872, 5536, 10671, 20569, 39648, 76424, 147312, 283953, 547337, 1055026, 2033628, 3919944, 7555935, 14564533, 28074040]

i=5
A001591
[0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 31, 61, 120, 236, 464, 912, 1793, 3525, 6930, 13624, 26784, 52656, 103519, 203513, 400096, 786568, 1546352, 3040048, 5976577, 11749641, 23099186]

i=6
[0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 63, 125, 248, 492, 976, 1936, 3840, 7617, 15109, 29970, 59448, 117920, 233904, 463968, 920319, 1825529, 3621088, 7182728, 14247536]

The smallest i for which there is a sequence is not in the OEIS is 14

I don't think it should be in the OEIS because its just the fibonacci i-step numbers and the first 13 are there. 

Question 4
Find GFseq(x/(1-x-x^a-x^b),x,100) where a is the second digit of RUID and b is the 7th digit of RUID.

Answer 4
a=8
b=2
GFseq(x/(1-x-x^8-x^2),x,100)
[0, 1, 1, 2, 3, 5, 8, 13, 21, 35, 57, 94, 154, 253, 415, 681, 1117, 1833, 3007, 4934, 8095, 13282, 21792, 35755, 58664, 96252, 157923, 259109, 425127, 697518, 1144437, 1877710, 3080811, 5054773, 8293507, 13607389, 22326023, 36630930, 60101390, 98610030, 161792231, 265457034, 435542772, 714607195, 1172475990, 1923714115, 3156291495, 5178615640, 8496699366, 13940772040, 22873014178, 37528393413, 61573883581, 101025991109, 165756166185, 271960772934, 446213638485, 732115183459, 1201201836122, 1970845412994, 3233621132697, 5305492536800, 8704869835682, 14282323145416, 23433406619583, 38447844948458, 63082453404163, 103501143765615, 169817218302475, 278623854604890, 457145942743047, 750052120493353, 1230631469855983, 2019131435297794, 3312845358557940, 5435477937621349, 8918140514481764, 14632242306708003, 24007528763932814, 39389823191134170, 64627983424922967, 106036938051354931, 173977766834835838, 285450182823812118, 468346090173129720, 768428515303649841, 1260782134240712375, 2068600472735496386, 3394010590401131728, 5568648001187983045, 9136636358423950611, 14990734542435745774, 24595716991032826105, 40354880048772221720, 66211379174045760200, 108634859695553478306, 178240249460000370234, 292443757156741831585, 479820642975166152430, 787255134674343729789, 1291671494640542708324]

The 101st term is 1291671494640542708324.