In the order of: A,ini, mod Mod 10: (All Andrew's Bressoud) [{[0, 0, 0], [0, 1, 0]}, [], [], 10], `Product side is:`, {1, 2, 3, 5, 7, 8, 9}, `mod `, 10 (in OEIS) -Andrew's Bressoud [1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 34, 44, 56, 71, 90, 112, 140, 174, 214, 263, 322, 392, 476, 576, 694, 834, 1000, 1194, 1423, 1692, 2005, 2372, 2800, 3296, 3874, 4544, 5318, 6214, 7248, 8438, 9808, 11383, 13188, 15258, 17628, 20334, 23426, 26952, 30966, 35536] [{[0, 0, 1], [1, 0, 0], [0, 0, 0, 0]}, [], [], 10], `1 is in Findprod` (in OEIS) [1, 1, 2, 3, 5, 5, 9, 11, 16, 20, 28, 34, 47, 57, 75, 92, 119, 143, 183, 220, 277, 332, 412, 491, 605, 718, 874, 1036, 1252, 1475, 1772, 2082, 2483, 2909, 3450, 4027, 4755, 5533, 6499, 7545, 8826, 10213, 11904, 13741, 15955, 18372, 21262, 24422, 28181, 32295, 37152] [{[0, 0, 0], [0, 1, 0]}, [], [], 10], `Product side is:`, {1, 2, 3, 5, 7, 8, 9}, `mod `, 10 (in OEIS) [1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 34, 44, 56, 71, 90, 112, 140, 174, 214, 263, 322, 392, 476, 576, 694, 834, 1000, 1194, 1423, 1692, 2005, 2372, 2800, 3296, 3874, 4544, 5318, 6214, 7248, 8438, 9808, 11383, 13188, 15258, 17628, 20334, 23426, 26952, 30966, 35536] [{[0, 0, 1], [1, 0, 0], [0, 0, 0, 0]}, [[1]], [], 10], `Product side is:`, {2, 3, 4, 5, 6, 7, 8}, `mod `, 10 [1, 0, 1, 1, 2, 2, 4, 4, 7, 7, 11, 12, 19, 20, 29, 33, 45, 51, 69, 78, 103, 118, 151, 174, 221, 253, 316, 365, 450, 518, 634, 729, 884, 1017, 1221, 1405, 1678, 1925, 2284, 2621, 3091, 3540, 4157, 4753, 5555, 6345, 7381, 8419, 9762, 11112, 12838] ############# Mod 12 [{[1, 0], [1, 1, 1]}, [[1]], [], 12], `Product side is:`, {2, 3, 4, 5, 6, 8, 9, 11, 12}, `mod `, 12 [1, 0, 1, 1, 2, 2, 4, 3, 7, 7, 10, 12, 18, 18, 28, 31, 42, 49, 65, 72, 99, 111, 141, 166, 209, 237, 302, 345, 425, 495, 601, 690, 847, 968, 1162, 1348, 1604, 1840, 2198, 2514, 2970, 3419, 4004, 4586, 5386, 6141, 7155, 8194, 9492, 10825, 12546] (What we discussed, seems to be new) Then: [{[0, 1], [1, 1, 1]},[[1,1],[3,2,1]],[],12], `Product side is:`, {1, 3, 4, 6, 7, 8, 9, 10, 12}, `mod `, 12 [1, 1, 1, 2, 3, 3, 5, 7, 9, 12, 16, 19, 26, 33, 40, 51, 66, 78, 98, 122, 148, 180, 222, 264, 322, 389, 463, 554, 669, 787, 937, 1115, 1315, 1547, 1832, 2141, 2515, 2949, 3439, 4006, 4686, 5428, 6302, 7317, 8464, 9767, 11301, 13003, 14972, 17227, 19773] #### [{[1], [0]}, [[2]],[{[2]}, {[3]}, {[2], [3]}], `Product side is:`, [-1, 1, -1, 0, -1, 0, -1, 0, -1, 1, -1, 0] (in OEIS) -Capparelli [1, 1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 5, 5, 5, 7, 8, 8, 11, 12, 12, 16, 17, 18, 23, 25, 26, 32, 35, 37, 45, 49, 52, 62, 67, 72, 85, 92, 98, 114, 124, 133, 153, 166, 178, 203, 220, 236, 268, 290, 311] [{[1], [0]}, [[1]],[{[2]}, {[3]}, {[2], [3]}], `Product side is:`, {2, 3, 9, 10}, `mod `, 12 (in OEIS) -Capparelli [1, 0, 1, 1, 1, 1, 2, 1, 2, 3, 3, 3, 5, 4, 6, 7, 7, 8, 11, 10, 13, 15, 16, 18, 23, 22, 27, 31, 33, 37, 45, 45, 53, 60, 64, 71, 84, 86, 99, 111, 119, 131, 151, 157, 178, 198, 212, 233, 264, 277, 310] ###################### [{},[],[{[1], [2]}, {[2]}, {[0], [3]}],12], `Product side is:`, [-1, -1, -1, 1, 0, -1, -1, -1, -1, 0, 0, -1] [1, 1, 2, 3, 3, 4, 6, 7, 10, 14, 16, 20, 26, 30, 39, 50, 58, 71, 87, 100, 123, 151, 175, 210, 251, 287, 343, 409, 471, 556, 652, 743, 870, 1017, 1163, 1354, 1568, 1779, 2056, 2370, 2692, 3099, 3551, 4011, 4588, 5235, 5911, 6742, 7661, 8615, 9775] [{}, [], [{[1], [2]}, {[0], [2], [3]}, {}], 12], `Product side is:`, {1, 3, 6, 7, 8, 9, 11, 12}, `mod `, 12. [1, 1, 1, 2, 2, 2, 4, 5, 6, 9, 10, 11, 16, 19, 22, 30, 35, 39, 51, 60, 69, 88, 102, 115, 143, 166, 189, 232, 268, 302, 363, 418, 474, 565, 648, 730, 859, 981, 1106, 1294, 1475, 1656, 1918, 2177, 2444, 2818, 3191, 3572, 4090, 4614, 5158] ### [[{[1, 1, 1], [1, 0, 1, 1], [1, 0, 1, 0, 1]}, [], [{[1], [2]}, {[0], [2], [3]}, {}], 12], `Product side is:`, {1, 3, 6, 7, 8, 9, 12}, `mod `, 12] [1, 1, 1, 2, 2, 2, 4, 5, 6, 9, 10, 11, 16, 19, 22, 30, 35, 39, 51, 60, 69, 88, 102, 115, 143, 166, 189, 232, 268, 302, 363, 418, 474, 565, 648, 730, 859, 981, 1106, 1294, 1475, 1656, 1918, 2177, 2444, 2818, 3191, 3572, 4090, 4614, 5158] ##(Same as above)## ### [{}, [], [{[1], [2]}, {[0], [2], [3]}, {[0], [3]}], 12], `Product side is:`, [-1, 0, -1, 1, 0, -1, -1, -1, -1, 0, 0, -1] [1, 1, 1, 2, 1, 1, 3, 3, 4, 7, 6, 6, 10, 10, 12, 19, 18, 19, 28, 28, 33, 48, 48, 52, 70, 71, 81, 111, 114, 125, 161, 165, 186, 242, 253, 279, 347, 360, 401, 503, 531, 586, 712, 745, 825, 1006, 1068, 1178, 1403, 1478, 1628] [{}, [[2]], [{[2]}, {[0], [3]}, {[1], [2]}], 12], `Product side is:`, [-1, 1, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1] [1, 1, 0, 1, 1, 1, 3, 3, 2, 4, 5, 5, 9, 10, 8, 13, 16, 16, 25, 28, 26, 37, 44, 46, 63, 72, 71, 93, 110, 116, 150, 171, 175, 219, 255, 273, 337, 383, 401, 485, 560, 603, 722, 818, 869, 1027, 1174, 1270, 1488, 1678, 1799] [{}, [[1], [2]], [{}, {[1], [2]}, {[0], [2], [3]}], 12], `Product side is:`, {3, 4, 5, 6, 9, 11, 12}, `mod `, 12 [1, 0, 0, 1, 1, 1, 2, 1, 2, 4, 3, 4, 7, 5, 7, 12, 11, 13, 19, 17, 23, 32, 30, 37, 50, 48, 60, 79, 79, 94, 119, 121, 148, 183, 187, 222, 272, 282, 335, 403, 423, 493, 585, 620, 726, 851, 902, 1043, 1217, 1300, 1499] 🧐 [{[1]}, [], [{[0], [3]}, {}, {}], 12],`Product side is:`, {1, 2, 4, 6, 8, 10, 11}, `mod `, 12 [1, 1, 2, 2, 4, 4, 7, 7, 12, 12, 19, 20, 30, 32, 46, 49, 69, 74, 101, 109, 146, 158, 208, 226, 293, 319, 408, 445, 562, 614, 767, 839, 1038, 1137, 1394, 1528, 1859, 2039, 2462, 2702, 3241, 3558, 4241, 4657, 5520, 6062, 7148, 7850, 9212, 10116, 11818] [{[1]}, [[1]], [{}, {}, {[0], [3]}],12], `Product side is:`, {2, 3, 6, 8, 9, 10, 12}, `mod `, 12 [1, 0, 1, 1, 1, 1, 3, 1, 4, 4, 5, 5, 10, 6, 13, 13, 16, 17, 28, 21, 37, 37, 46, 49, 72, 61, 94, 96, 117, 126, 172, 157, 223, 230, 277, 299, 388, 372, 498, 519, 617, 667, 835, 827, 1062, 1115, 1310, 1418, 1727, 1750, 2176] [{[1]}, [[1]], [{}, {[0], [3]}, {}], 12], `Product side is:`, {2, 3, 4, 6, 9, 10, 12}, `mod `, 12 [1, 0, 1, 1, 2, 1, 4, 2, 5, 5, 8, 6, 14, 10, 18, 18, 27, 23, 42, 35, 54, 55, 77, 71, 112, 102, 144, 149, 199, 192, 277, 266, 354, 370, 476, 474, 642, 638, 815, 859, 1074, 1092, 1414, 1438, 1782, 1890, 2308, 2383, 2983, 3083, 3732] [{[1]}, [[1]], [{}, {[0], [3]}, {[0], [3]}], 12], `Product side is:`, {2, 3, 6, 9, 10, 12}, `mod `, 12 [1, 0, 1, 1, 1, 1, 3, 1, 3, 4, 4, 4, 9, 5, 10, 12, 12, 13, 23, 16, 26, 31, 32, 35, 55, 43, 63, 74, 77, 85, 122, 104, 141, 164, 172, 190, 258, 232, 300, 345, 364, 402, 521, 488, 608, 694, 735, 811, 1017, 980, 1189] [{[1, 2], [2, 1]},[[1], [2]], [{}, {[0], [1], [2], [3]}, {[2]}],12], `Product side is:`, [0, 0, -1, -1, -1, -1, 0, 1, -1, -1, -1, -1] [1, 0, 0, 1, 1, 1, 2, 1, 1, 4, 4, 3, 6, 5, 6, 12, 11, 10, 17, 17, 19, 30, 30, 29, 44, 47, 51, 72, 74, 76, 106, 115, 124, 163, 173, 182, 239, 262, 282, 354, 382, 408, 512, 564, 608, 739, 805, 867, 1055, 1163, 1256] [[{[1, 2], [2, 1], [2, 2]}, [], [{[1], [2]}, {[2]}, {[0], [3]}], 12], `Product side is:`, [-1, -1, -1, 1, 0, -1, -1, -1, -1, 0, 0, -1] [1, 1, 2, 3, 3, 4, 6, 7, 10, 14, 16, 20, 26, 30, 39, 50, 58, 71, 87, 100, 123, 151, 175, 210, 251, 287, 343, 409, 471, 556, 652, 743, 870, 1017, 1163, 1354, 1568, 1779, 2056, 2370, 2692, 3099, 3551, 4011, 4588, 5235, 5911, 6742, 7661, 8615, 9775] (same as [{},[],[{[1], [2]}, {[2]}, {[0], [3]}],12]) ### [[{[1, 1, 1], [1, 1, 0, 1, 1]}, [], [{[1], [2]}, {[2]}, {[0], [3]}], 12], `Product side is:`, [-1, -1, -1, 1, 0, -1, -1, -1, -1, 0, 0, -1]] [1, 1, 2, 3, 3, 4, 6, 7, 10, 14, 16, 20, 26, 30, 39, 50, 58, 71, 87, 100, 123, 151, 175, 210, 251, 287, 343, 409, 471, 556, 652, 743, 870, 1017, 1163, 1354, 1568, 1779, 2056, 2370, 2692, 3099, 3551, 4011, 4588, 5235, 5911, 6742, 7661, 8615, 9775] ###(same as above)### ### [{[1, 2], [2, 0], [2, 1], [2, 2]},[[2]],[{[2]}, {[0], [3]}, {[0], [1], [2], [3]}],12], `Product side is:`, [-1, 1, -1, 0, -1, -1, -1, 0, -1, 1, -1, -1] [1, 1, 0, 1, 1, 1, 3, 3, 2, 4, 4, 4, 9, 9, 7, 12, 13, 13, 23, 24, 21, 32, 34, 35, 55, 58, 54, 76, 82, 85, 122, 130, 127, 169, 182, 191, 259, 277, 277, 355, 384, 405, 524, 563, 575, 714, 772, 818, 1025, 1103, 1140] [{[1, 2], [2, 0], [2, 1]}, [[1], [2]], [{}, {[0], [1], [2], [3]}, {[0], [2], [3]}],12], `Product side is:`, [0, 0, -1, -1, -1, -1, 0, 1, -1, 0, -1, -1] [1, 0, 0, 1, 1, 1, 2, 1, 1, 4, 3, 3, 6, 4, 5, 11, 9, 9, 16, 13, 15, 27, 23, 24, 38, 34, 39, 61, 55, 58, 86, 81, 91, 131, 122, 131, 183, 178, 198, 268, 258, 279, 372, 370, 408, 530, 521, 566, 728, 735, 807] And many more of this form...in the folder testNew5 #########Oct. 18########### #In KR paper [[{[0, 0], [1, 0], [0, 1, 1], [1, 1, 1], [0, 2, 0, 1]}, [[1]], [], 12], `Product side is:`, {2, 3, 4, 5, 8, 9, 11}, `mod `, 12] [1, 0, 1, 1, 2, 2, 3, 3, 6, 6, 8, 10, 13, 15, 20, 23, 30, 35, 43, 51, 64, 73, 89, 105, 126, 147, 175, 203, 242, 280, 328, 381, 447, 513, 598, 689, 798, 916, 1056, 1208, 1393, 1588, 1818, 2074, 2370, 2691, 3067, 3478, 3953, 4474, 5068] [[{[1, 1], [0, 0, 0], [1, 0, 1], [1, 0, 0, 1]}, [], [], 12], `Product side is:`, {1, 2, 3, 5, 7, 9, 10, 11}, `mod `, 12] [1, 1, 2, 3, 4, 6, 8, 11, 14, 19, 25, 32, 41, 52, 66, 83, 103, 128, 157, 193, 236, 287, 348, 420, 506, 607, 726, 866, 1030, 1222, 1446, 1707, 2010, 2362, 2770, 3242, 3787, 4415, 5138, 5969, 6923, 8016, 9267, 10697, 12330, 14192, 16312, 18724, 21465, 24576, 28104] ### [[{[0, 0, 0]}, [], [{[0]}, {}, {}], 12], `Product side is:`, {1, 2, 3, 5, 7, 9, 10, 11}, `mod `, 12] [1, 1, 2, 3, 4, 6, 8, 11, 14, 19, 25, 32, 41, 52, 66, 83, 103, 128, 157, 193, 236, 287, 348, 420, 506, 607, 726, 866, 1030, 1222, 1446, 1707, 2010, 2362, 2770, 3242, 3787, 4415, 5138, 5969, 6923, 8016, 9267, 10697, 12330, 14192, 16312, 18724, 21465, 24576, 28104] ###(Same as above)### #### [[{[0, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}, [], [], 14], `Product side is:`, {1, 2, 3, 4, 5, 7, 9, 10, 11, 12, 13}, `mod `, 14] [1, 1, 2, 3, 5, 7, 10, 14, 19, 26, 35, 46, 61, 79, 102, 131, 167, 211, 266, 333, 415, 515, 636, 782, 959, 1171, 1425, 1729, 2091, 2521, 3033, 3637, 4351, 5193, 6183, 7345, 8708, 10301, 12161, 14331, 16856, 19789, 23195, 27139, 31703, 36978, 43063, 50075, 58148, 67426, 78079] #Andrews Bousoud ######Oct. 20######### [[{[0, 1, 0], [0, 0, 0, 0, 0]}, [], [], 12], `Product side is:`, [-1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 0] [1, 1, 2, 3, 5, 7, 9, 13, 18, 24, 32, 42, 55, 71, 91, 116, 147, 185, 231, 288, 357, 440, 540, 661, 807, 980, 1186, 1432, 1724, 2069, 2476, 2956, 3521, 4183, 4958, 5865, 6923, 8155, 9587, 11251, 13180, 15411, 17990, 20967, 24399, 28348, 32886, 38098, 44075, 50919, 58748] (in OEIS) ## [[{[0, 1, 0]}, [], [{[0]}, {}, {}], 12], `Product side is:`, [-1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 0]] [1, 1, 2, 3, 5, 7, 9, 13, 18, 24, 32, 42, 55, 71, 91, 116, 147, 185, 231, 288, 357, 440, 540, 661, 807, 980, 1186, 1432, 1724, 2069, 2476, 2956, 3521, 4183, 4958, 5865, 6923, 8155, 9587, 11251, 13180, 15411, 17990, 20967, 24399, 28348, 32886, 38098, 44075, 50919, 58748] ##(Same as above)## ## #### [[{[0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}, [], [], 11], `Product side is:`, {1, 2, 3, 4, 7, 8, 9, 10}, `mod `, 11] [1, 1, 2, 3, 5, 6, 9, 12, 17, 22, 30, 38, 51, 64, 83, 104, 133, 164, 207, 254, 316, 386, 475, 576, 704, 848, 1027, 1232, 1483, 1768, 2116, 2512, 2989, 3534, 4184, 4926, 5808, 6812, 7996, 9348, 10932, 12735, 14842, 17238, 20022, 23188, 26850, 31008, 35805, 41242, 47490]. (in OEIS) Gordon-Andrews [[{[0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}, [[1]], [], 11], `Product side is:`, {2, 3, 4, 5, 6, 7, 8, 9}, `mod `, 11] [1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 11, 13, 19, 22, 30, 36, 47, 56, 73, 86, 110, 131, 163, 194, 241, 284, 348, 412, 499, 588, 709, 832, 996, 1168, 1387, 1622, 1919, 2235, 2631, 3060, 3584, 4156, 4852, 5610, 6525, 7530, 8724, 10044, 11607, 13328, 15355] Gordon-Andrews (in OEIS) ######Oct. 21######### 🧐 [[{[0, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, [], [], 15], `Product side is:`, {1, 2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 14}, `mod `, 15] [1, 1, 2, 3, 5, 7, 10, 14, 20, 26, 36, 47, 63, 81, 106, 135, 174, 219, 278, 347, 436, 539, 670, 823, 1014, 1237, 1512, 1834, 2227, 2685, 3240, 3887, 4665, 5570, 6650, 7906, 9396, 11124, 13164, 15526, 18302, 21508, 25260, 29587, 34630, 40434, 47174, 54918, 63882, 74159, 86020] (In OEIS, could be interesting) ################### [[{[0, 0, 0], [0, 0, 1], [0, 1, 0], [1, 0, 0]}, [], [], 9], `Product side is:`, {1, 2, 3, 6, 7, 8}, `mod `, 9] [1, 1, 2, 3, 4, 5, 8, 10, 14, 18, 24, 30, 40, 49, 63, 78, 98, 120, 150, 182, 224, 271, 330, 396, 480, 572, 687, 817, 974, 1151, 1367, 1608, 1898, 2226, 2614, 3053, 3573, 4157, 4844, 5620, 6524, 7544, 8731, 10066, 11611, 13353, 15356, 17612, 20203, 23112, 26441] [[{[0, 0, 0], [0, 0, 1], [0, 1, 0], [1, 0, 0]}, [[1]], [], 9], `Product side is:`, {2, 3, 4, 5, 6, 7}, `mod `, 9] [1, 0, 1, 1, 2, 2, 4, 4, 6, 7, 10, 12, 17, 19, 26, 31, 40, 47, 61, 71, 90, 106, 131, 154, 190, 222, 270, 317, 381, 445, 533, 620, 737, 857, 1011, 1173, 1379, 1593, 1863, 2151, 2503, 2881, 3343, 3837, 4435, 5083, 5853, 6693, 7688, 8769, 10043] ######Oct. 24####### [[{}, [[1]], [{}, {[2], [1, 0], [1, 1]}], 12], `Product side is:`, {2, 3, 4, 5, 6, 9, 10, 11, 12}, `mod `, 12] [1, 0, 1, 1, 2, 2, 4, 3, 6, 7, 10, 11, 17, 17, 26, 30, 39, 45, 61, 67, 90, 104, 130, 151, 192, 217, 274, 317, 385, 447, 547, 624, 760, 877, 1044, 1207, 1441, 1647, 1960, 2252, 2642, 3038, 3566, 4069, 4764, 5449, 6319, 7228, 8379, 9531, 11026] [[{}, [], [{[0, 0]}, {[0]}], 12], `Product side is:`, [-1, 0, -1, -1, -1, 1, -1, -1, -1, 0, -1, 0]] [1, 1, 1, 2, 3, 4, 4, 6, 9, 11, 13, 17, 22, 27, 32, 40, 51, 61, 72, 88, 108, 128, 150, 180, 217, 255, 297, 351, 416, 485, 562, 657, 770, 891, 1026, 1190, 1380, 1587, 1818, 2092, 2409, 2754, 3140, 3591, 4106, 4672, 5302, 6030, 6858, 7767, 8779] [[{}, [], [{[0]}, {[0, 0]}], 12], `Product side is:`, {1, 2, 5, 6, 7, 10, 11}, `mod `, 12] [1, 1, 2, 2, 3, 4, 6, 8, 10, 12, 16, 20, 26, 32, 40, 48, 59, 72, 88, 106, 128, 152, 182, 216, 258, 305, 360, 422, 496, 580, 680, 792, 922, 1068, 1238, 1432, 1656, 1908, 2196, 2520, 2892, 3312, 3792, 4330, 4940, 5624, 6400, 7272, 8258, 9361, 10602] (exact form in OEIS) #### [[{[1, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 1, 1]}, [], [{[0], [2], [3]}, {}, {[1], [2]}], 12], `Product side is:`, {1, 2, 5, 6, 7, 10, 11}, `mod `, 12] [1, 1, 2, 2, 3, 4, 6, 8, 10, 12, 16, 20, 26, 32, 40, 48, 59, 72, 88, 106, 128, 152, 182, 216, 258, 305, 360, 422, 496, 580, 680, 792, 922, 1068, 1238, 1432, 1656, 1908, 2196, 2520, 2892, 3312, 3792, 4330, 4940, 5624, 6400, 7272, 8258, 9361, 10602] ##(Same as above)## ##### [[{}, [], [{[0, 1]}, {[2], [1, 1]}], 12], `Product side is:`, {1, 2, 3, 6, 7, 8, 9, 10, 12}, `mod `, 12] [1, 1, 2, 3, 4, 5, 8, 10, 14, 19, 25, 31, 42, 52, 67, 85, 107, 131, 166, 202, 250, 307, 376, 453, 555, 665, 803, 965, 1158, 1376, 1649, 1951, 2316, 2740, 3239, 3804, 4488, 5253, 6157, 7198, 8409, 9780, 11402, 13224, 15344, 17768, 20561, 23717, 27391, 31521, 36272] [[{[0]}, [], [{[1], [2, 2]}, {[1, 2], [2, 1]}], 12], `Product side is:`, {1, 4, 5, 9, 11}, `mod `, 12] [1, 1, 1, 1, 2, 3, 3, 3, 4, 6, 7, 8, 9, 12, 14, 16, 19, 23, 27, 30, 35, 42, 49, 55, 62, 73, 85, 96, 108, 124, 142, 160, 180, 205, 233, 261, 292, 330, 373, 417, 464, 520, 584, 651, 723, 806, 900, 999, 1106, 1228, 1366] (in KR paper, identity 4.1) [[{[0]}, [], [{[2], [1, 1]}, {[1, 2], [3, 2]}], 20], `Product side is:`, [-1, 0, -1, 0, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 0, -1, 0, -1, 0]] [1, 1, 1, 2, 2, 3, 3, 4, 6, 7, 8, 10, 13, 15, 17, 21, 26, 30, 35, 41, 49, 57, 65, 76, 90, 103, 117, 136, 157, 179, 203, 232, 267, 303, 341, 388, 442, 498, 559, 632, 715, 802, 897, 1008, 1133, 1267, 1411, 1578, 1767, 1966, 2184] [[{[0]}, [[2]], [{[2], [1, 1]}, {[1, 2], [3, 2]}], 20], `Product side is:`[-1, 1, -1, -1, -1, 0, -1, 0, -1, 1, -1, 0, -1, 0, -1, -1, -1, 1, -1, 0] [1, 1, 0, 1, 2, 2, 2, 3, 4, 5, 5, 6, 9, 10, 11, 14, 18, 20, 22, 27, 33, 38, 42, 49, 60, 68, 75, 88, 104, 117, 131, 151, 175, 198, 220, 251, 289, 324, 360, 409, 466, 520, 578, 651, 735, 820, 909, 1017, 1144, 1271, 1404] (found by hand by adding a initial condition) [[{}, [], [{[0, 1], [1, 2]}, {[0], [1, 1], [2, 2]}], 12], `Product side is:`, {1, 3, 4, 7, 8, 9, 10, 12}, `mod `, 12] [1, 1, 1, 2, 3, 3, 4, 6, 8, 10, 13, 16, 21, 26, 31, 39, 50, 59, 71, 88, 107, 127, 153, 183, 220, 261, 307, 364, 434, 507, 593, 699, 820, 952, 1110, 1292, 1502, 1739, 2008, 2320, 2685, 3085, 3541, 4074, 4678, 5346, 6115, 6990, 7980, 9090, 10342] ######Oct. 25####### [[{[0, 0, 0]}, [], [{}, {[0]}, {[0]}], 12], `Product side is:`, {1, 3, 5, 6, 7, 9, 11}, `mod `, 12] [1, 1, 1, 2, 2, 3, 5, 6, 7, 10, 12, 15, 20, 24, 29, 37, 44, 53, 67, 79, 94, 115, 135, 160, 193, 226, 265, 315, 367, 428, 505, 585, 678, 792, 913, 1054, 1224, 1405, 1613, 1860, 2127, 2433, 2792, 3181, 3623, 4137, 4697, 5332, 6064, 6863, 7764] [[{[0, 0, 0]}, [], [{[0]}, {[0]}, {}], 12], `Product side is:`, [-1, 0, -1, -1, -1, 0, -1, 1, -1, -1, -1, 0]] [1, 1, 1, 2, 3, 4, 5, 7, 8, 11, 15, 18, 22, 28, 35, 43, 53, 64, 77, 94, 113, 135, 162, 192, 227, 270, 319, 374, 440, 515, 601, 702, 817, 947, 1098, 1271, 1466, 1691, 1947, 2235, 2565, 2939, 3360, 3839, 4381, 4989, 5676, 6452, 7322, 8302, 9404] [[{[0, 0, 0], [0, 0, 1, 0], [1, 1, 0, 1, 0]}, [], [{[0]}, {[0]}, {}], 12], `Product side is:`, [-1, 0, -1, -1, -1, 0, -1, 1, -1, -1, -1, 0]] [1, 1, 1, 2, 3, 4, 5, 7, 8, 11, 15, 18, 22, 28, 35, 43, 53, 64, 77, 94, 113, 135, 162, 192, 227, 270, 319, 374, 440, 515, 601, 702, 817, 947, 1098, 1271, 1466, 1691, 1947, 2235, 2565, 2939, 3360, 3839, 4381, 4989, 5676, 6452, 7322, 8302, 9404] [[{[0, 0, 0], [0, 0, 1, 0], [1, 0, 1, 1, 0]}, [], [{[0]}, {[0]}, {}], 12], `Product side is:`, [-1, 0, -1, -1, -1, 0, -1, 1, -1, -1, -1, 0]] [1, 1, 1, 2, 3, 4, 5, 7, 8, 11, 15, 18, 22, 28, 35, 43, 53, 64, 77, 94, 113, 135, 162, 192, 227, 270, 319, 374, 440, 515, 601, 702, 817, 947, 1098, 1271, 1466, 1691, 1947, 2235, 2565, 2939, 3360, 3839, 4381, 4989, 5676, 6452, 7322, 8302, 9404] [[{[0, 0, 0], [0, 0, 1, 0], [1, 0, 1, 0, 1]}, [], [{[0]}, {[0]}, {}], 12], `Product side is:`, [-1, 0, -1, -1, -1, 0, -1, 1, -1, -1, -1, 0]] [1, 1, 1, 2, 3, 4, 5, 7, 8, 11, 15, 18, 22, 28, 35, 43, 53, 64, 77, 94, 113, 135, 162, 192, 227, 270, 319, 374, 440, 515, 601, 702, 817, 947, 1098, 1271, 1466, 1691, 1947, 2235, 2565, 2939, 3360, 3839, 4381, 4989, 5676, 6452, 7322, 8302, 9404] [[{[0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0, 1]}, [], [{[0]}, {[0]}, {}], 12], `Product side is:`, [-1, 0, -1, -1, -1, 0, -1, 1, -1, -1, -1, 0]] [1, 1, 1, 2, 3, 4, 5, 7, 8, 11, 15, 18, 22, 28, 35, 43, 53, 64, 77, 94, 113, 135, 162, 192, 227, 270, 319, 374, 440, 515, 601, 702, 817, 947, 1098, 1271, 1466, 1691, 1947, 2235, 2565, 2939, 3360, 3839, 4381, 4989, 5676, 6452, 7322, 8302, 9404] [[{[0, 0, 0], [0, 0, 1, 0], [0, 0, 1, 1, 0]}, [], [{[0]}, {[0]}, {}], 12], `Product side is:`, [-1, 0, -1, -1, -1, 0, -1, 1, -1, -1, -1, 0]] [1, 1, 1, 2, 3, 4, 5, 7, 8, 11, 15, 18, 22, 28, 35, 43, 53, 64, 77, 94, 113, 135, 162, 192, 227, 270, 319, 374, 440, 515, 601, 702, 817, 947, 1098, 1271, 1466, 1691, 1947, 2235, 2565, 2939, 3360, 3839, 4381, 4989, 5676, 6452, 7322, 8302, 9404] [[{[0, 0, 0]}, [], [{[0]}, {}, {[0]}], 12], `Product side is:`, [-1, -1, -1, 1, -1, 0, -1, -1, -1, 0, -1, 0]] [1, 1, 2, 3, 3, 5, 6, 8, 11, 14, 18, 23, 28, 35, 44, 54, 66, 81, 97, 117, 142, 169, 203, 242, 286, 339, 400, 470, 553, 648, 756, 882, 1026, 1190, 1381, 1598, 1844, 2127, 2447, 2810, 3226, 3695, 4226, 4829, 5508, 6274, 7141, 8115, 9210, 10445, 11827] [[{[0, 0, 0], [0, 0, 1, 0], [1, 1, 0, 1, 0]}, [], [{[0]}, {}, {[0]}], 12], `Product side is:`, [-1, -1, -1, 1, -1, 0, -1, -1, -1, 0, -1, 0]] [1, 1, 2, 3, 3, 5, 6, 8, 11, 14, 18, 23, 28, 35, 44, 54, 66, 81, 97, 117, 142, 169, 203, 242, 286, 339, 400, 470, 553, 648, 756, 882, 1026, 1190, 1381, 1598, 1844, 2127, 2447, 2810, 3226, 3695, 4226, 4829, 5508, 6274, 7141, 8115, 9210, 10445, 11827] [[{[0, 0, 0], [0, 0, 1, 0], [1, 0, 1, 1, 0]}, [], [{[0]}, {}, {[0]}], 12], `Product side is:`, [-1, -1, -1, 1, -1, 0, -1, -1, -1, 0, -1, 0]] [1, 1, 2, 3, 3, 5, 6, 8, 11, 14, 18, 23, 28, 35, 44, 54, 66, 81, 97, 117, 142, 169, 203, 242, 286, 339, 400, 470, 553, 648, 756, 882, 1026, 1190, 1381, 1598, 1844, 2127, 2447, 2810, 3226, 3695, 4226, 4829, 5508, 6274, 7141, 8115, 9210, 10445, 11827] [[{[0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0, 1]}, [], [{[0]}, {}, {[0]}], 12], `Product side is:`, [-1, -1, -1, 1, -1, 0, -1, -1, -1, 0, -1, 0]] [1, 1, 2, 3, 3, 5, 6, 8, 11, 14, 18, 23, 28, 35, 44, 54, 66, 81, 97, 117, 142, 169, 203, 242, 286, 339, 400, 470, 553, 648, 756, 882, 1026, 1190, 1381, 1598, 1844, 2127, 2447, 2810, 3226, 3695, 4226, 4829, 5508, 6274, 7141, 8115, 9210, 10445, 11827] [[{[0, 0, 0]}, [], [{}, {[0]}, {}], 12], `Product side is:`, [-1, 0, -1, -1, -1, -1, -1, 1, -1, -1, -1, 0]] [1, 1, 1, 2, 3, 4, 6, 8, 9, 13, 18, 22, 28, 36, 44, 56, 71, 86, 106, 131, 158, 193, 236, 282, 338, 408, 485, 578, 691, 815, 962, 1139, 1338, 1570, 1845, 2154, 2511, 2932, 3407, 3953, 4590, 5307, 6126, 7077, 8151, 9372, 10777, 12360, 14154, 16211, 18529] [[{[0, 0, 0]}, [], [{}, {}, {[0]}], 12], `Product side is:`, [-1, -1, -1, 1, -1, -1, -1, -1, -1, 0, -1, 0]] [1, 1, 2, 3, 3, 5, 7, 9, 13, 17, 21, 28, 35, 44, 57, 71, 87, 109, 133, 162, 201, 243, 293, 356, 425, 509, 612, 727, 864, 1027, 1210, 1427, 1684, 1974, 2314, 2711, 3158, 3680, 4286, 4970, 5764, 6676, 7705, 8892, 10251, 11785, 13545, 15548, 17803, 20380, 23303] [[{[0, 1, 0]}, [], [{}, {[0]}, {}], 12], `Product side is:`, {1, 3, 4, 5, 6, 7, 9, 11, 12}, `mod `, 12] [1, 1, 1, 2, 3, 4, 6, 8, 10, 14, 18, 23, 31, 39, 48, 62, 78, 96, 121, 149, 181, 224, 273, 330, 403, 486, 581, 701, 840, 999, 1194, 1418, 1675, 1986, 2344, 2755, 3245, 3806, 4447, 5206, 6077, 7070, 8232, 9560, 11072, 12831, 14838, 17119, 19754, 22750, 26146] ############Family 1.1############ [{[0, 0, 0]}, [], [{[0]}, {[0]}, {}], `Product side is:`, [-1, 0, -1, -1, -1, 0, -1, 1, -1, -1, -1, 0]] [1, 1, 1, 2, 3, 4, 5, 7, 8, 11, 15, 18, 22, 28, 35, 43, 53, 64, 77, 94, 113, 135, 162, 192, 227, 270, 319, 374, 440, 515, 601, 702, 817, 947, 1098, 1271, 1466, 1691, 1947, 2235, 2565, 2939, 3360, 3839, 4381, 4989, 5676, 6452, 7322, 8302, 9404] #####4 zeros##### [{[0,0,0,0]}, [], [{[0]}, {[0]}, {}],30], `Product side is:`, {1, 3, 4, 5, 7, 9, 11, 13, 15, 16, 17, 19, 21, 22, 23, 27, 28, 29}, `mod `, 30 [1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 15, 19, 24, 30, 37, 46, 57, 69, 84, 102, 123, 148, 178, 212, 252, 299, 354, 418, 492, 577, 676, 791, 922, 1073, 1247, 1446, 1673, 1934, 2231, 2569, 2953, 3390, 3887, 4450, 5087, 5807, 6622, 7540, 8576, 9744, 11057] {[0,0,0,0,0]}, [], [{[0]}, {[0]}, {}], `Product side is:`, [-1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 1, -1, 0, -1, -1, -1, 0] (18 elements) [1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 16, 20, 24, 31, 39, 48, 59, 72, 88, 107, 130, 156, 187, 224, 267, 318, 377, 445, 525, 618, 725, 849, 992, 1156, 1345, 1563, 1812, 2096, 2422, 2793, 3216, 3698, 4246, 4867, 5572, 6371, 7274, 8295, 9447, 10747, 12212] {[0,0,0,0,0,0]}, [], [{[0]}, {[0]}, {}] `Product side is:`, [-1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, 1, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, 0, 0, -1, 0, -1, -1, -1, 0] [1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 16, 20, 25, 32, 39, 49, 61, 74, 90, 110, 134, 161, 194, 232, 276, 330, 392, 463, 547, 644, 757, 888, 1039, 1212, 1412, 1642, 1905, 2208, 2554, 2947, 3398, 3912, 4495, 5159, 5912, 6765, 7732, 8827, 10062, 11458, 13033] ###7 zeros##### [{[0,0,0,0,0,0,0]}, [], [{[0]}, {[0]}, {}], 24], `Product side is:`, {1, 3, 4, 5, 7, 9, 10, 11, 13, 15, 17, 19, 21, 22, 23}, `mod `, 24 [1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 16, 20, 25, 32, 40, 50, 61, 75, 92, 112, 136, 164, 198, 237, 283, 338, 401, 475, 562, 662, 779, 914, 1070, 1250, 1458, 1697, 1970, 2285, 2645, 3056, 3526, 4061, 4671, 5365, 6153, 7047, 8060, 9207, 10504, 11970, 13624] {[0,0,0,0,0,0,0,0]}, [], [{[0]}, {[0]}, {}], `Product side is:`, [-1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 1, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, 0, -1, -1, 0, -1, 0, -1, -1, -1, 0] [1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 16, 20, 25, 32, 40, 50, 62, 76, 92, 113, 138, 166, 200, 240, 287, 343, 408, 483, 571, 674, 794, 932, 1092, 1276, 1489, 1735, 2016, 2339, 2709, 3132, 3616, 4168, 4797, 5512, 6326, 7249, 8296, 9483, 10824, 12341, 14055] {[0,0,0,0,0,0,0,0,0]}, [], [{[0]}, {[0]}, {}],`Product side is:`, [-1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, 1, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0] [1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 16, 20, 25, 32, 40, 50, 62, 76, 93, 114, 138, 167, 202, 242, 289, 346, 412, 488, 578, 682, 803, 944, 1107, 1294, 1511, 1761, 2047, 2377, 2755, 3186, 3680, 4244, 4886, 5618, 6451, 7395, 8467, 9683, 11058, 12614, 14371] ###10 zeros##### {[0,0,0,0,0,0,0,0,0,0]}, [], [{[0]}, {[0]}, {}] `Product side is:`, {1, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 17, 19, 21, 23, 25, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 41, 43, 45, 46, 47, 49, 51, 52, 53, 57, 58, 59, 61, 63, 64, 65}, `mod `, 66 [1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 16, 20, 25, 32, 40, 50, 62, 76, 93, 114, 139, 168, 202, 243, 291, 348, 414, 491, 582, 687, 810, 952, 1116, 1306, 1526, 1779, 2069, 2403, 2786, 3224, 3726, 4298, 4950, 5694, 6540, 7501, 8592, 9828, 11228, 12813, 14604] ###13 zeros### `Product side is:`, {1, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 17, 19, 21, 22, 23, 25, 27, 29, 31, 33, 34, 35, 37, 39, 40, 41}, `mod `, 42 ###16 zeros### `Product side is:`, {1, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 17, 19, 21, 22, 23, 25, 27, 28, 29, 31, 33, 35, 37, 39, 40, 41, 43, 45, 46, 47, 49, 51, 52, 53, 55, 57, 58, 59, 61, 63, 64, 65, 67, 69, 70, 71, 73, 75, 76, 77, 79, 81, 82, 83, 87, 88, 89}, `mod `, 90 #####19 zeros### `Product side is:`, {1, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 17, 19, 21, 22, 23, 25, 27, 28, 29, 31, 33, 34, 35, 37, 39, 41, 43, 45, 46, 47, 49, 51, 52, 53, 55, 57, 58, 59}, `mod `, 60 #####22 zeros### `Product side is:`, {1, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 17, 19, 21, 22, 23, 25, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 41, 43, 45, 47, 49, 51, 52, 53}, `mod `, 54 ###################### #30,24,66,42,90,60,54# ###################### #########Family 1.2########## [{[0$3]}, [], [{}, {[0]}, {[0]}], 12], `Product side is:`, {1, 3, 5, 6, 7, 9, 11}, `mod `, 12 [1, 1, 1, 2, 2, 3, 5, 6, 7, 10, 12, 15, 20, 24, 29, 37, 44, 53, 67, 79, 94, 115, 135, 160, 193, 226, 265, 315, 367, 428, 505, 585, 678, 792, 913, 1054, 1224, 1405, 1613, 1860, 2127, 2433, 2792, 3181, 3623, 4137, 4697, 5332, 6064, 6863, 7764] [{[0$4]}, [], [{}, {[0]}, {[0]}], 30], `Product side is:`, {1, 3, 5, 6, 7, 9, 11, 12, 13, 17, 18, 19, 21, 23, 24, 25, 27, 29}, `mod `, 30 [1, 1, 1, 2, 2, 3, 5, 6, 7, 10, 12, 15, 20, 24, 29, 37, 44, 53, 67, 79, 94, 115, 135, 160, 193, 226, 265, 315, 367, 428, 505, 585, 678, 792, 913, 1054, 1224, 1405, 1613, 1860, 2127, 2433, 2792, 3181, 3623, 4137, 4697, 5332, 6064, 6863, 7764] [{[0$5]}, [], [{}, {[0]}, {[0]}], 18], `Product side is:`, {1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17}, `mod `, 18 [{[0$6]}, [], [{}, {[0]}, {[0]}], 42] `Product side is:`, {1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19, 23, 24, 25, 27, 29, 30, 31, 33, 35, 36, 37, 39, 41}, `mod `, 42 [{[0$7]}, [], [{}, {[0]}, {[0]}], 24] `Product side is:`, {1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19, 21, 23}, `mod `, 24 etc. ########Family 1.3########## [[{[0, 0, 0]}, [], [{[0]}, {}, {[0]}], 12], `Product side is:`, [-1, -1, -1, 1, -1, 0, -1, -1, -1, 0, -1, 0]] [1, 1, 2, 3, 3, 5, 6, 8, 11, 14, 18, 23, 28, 35, 44, 54, 66, 81, 97, 117, 142, 169, 203, 242, 286, 339, 400, 470, 553, 648, 756, 882, 1026, 1190, 1381, 1598, 1844, 2127, 2447, 2810, 3226, 3695, 4226, 4829, 5508, 6274, 7141, 8115, 9210, 10445, 11827] 0$4: `Product side is:`, {1, 2, 3, 7, 8, 9, 11, 13, 14, 15, 17, 19, 21, 23, 25, 26, 27, 29}, `mod `, 30 [1, 1, 2, 3, 4, 5, 7, 9, 12, 16, 20, 26, 32, 40, 50, 62, 76, 94, 114, 138, 166, 200, 239, 286, 340, 404, 478, 564, 664, 780, 914, 1068, 1247, 1451, 1686, 1955, 2263, 2614, 3016, 3473, 3994, 4586, 5258, 6019, 6882, 7857, 8959, 10204, 11606, 13186, 14963] 0$5: `Product side is:`, [-1, -1, -1, 0, -1, 1, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0] [1, 1, 2, 3, 4, 6, 7, 10, 13, 17, 22, 28, 35, 44, 55, 68, 84, 103, 126, 153, 185, 223, 268, 321, 382, 455, 539, 637, 752, 884, 1039, 1216, 1421, 1657, 1928, 2240, 2597, 3006, 3473, 4006, 4614, 5305, 6091, 6984, 7996, 9143, 10440, 11906, 13562, 15429, 17533] etc. ######Family 2.1############ [[{[0, 0, 0]}, [], [{[0]}, {}, {}], 12], `Product side is:`, {1, 2, 3, 5, 7, 9, 10, 11}, `mod `, 12 [1, 1, 2, 3, 4, 6, 8, 11, 14, 19, 25, 32, 41, 52, 66, 83, 103, 128, 157, 193, 236, 287, 348, 420, 506, 607, 726, 866, 1030, 1222, 1446, 1707, 2010, 2362, 2770, 3242, 3787, 4415, 5138, 5969, 6923, 8016, 9267, 10697, 12330, 14192, 16312, 18724, 21465, 24576, 28104] 0$4: `Product side is:`, {1, 2, 3, 4, 7, 8, 9, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 26, 27, 28, 29}, `mod `, 30 [1, 1, 2, 3, 5, 6, 9, 12, 17, 22, 29, 38, 49, 62, 79, 100, 126, 157, 195, 241, 296, 362, 442, 537, 650, 784, 943, 1130, 1351, 1610, 1916, 2272, 2690, 3175, 3742, 4398, 5161, 6043, 7065, 8242, 9600, 11162, 12958, 15018, 17381, 20086, 23179, 26710, 30739, 35329, 40552] 0$5: `Product side is:`, [-1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 0] [1, 1, 2, 3, 5, 7, 9, 13, 18, 24, 32, 42, 54, 70, 89, 113, 142, 178, 223, 276, 341, 419, 513, 626, 760, 921, 1111, 1337, 1604, 1919, 2290, 2725, 3235, 3832, 4528, 5340, 6285, 7381, 8653, 10125, 11827, 13790, 16052, 18657, 21650, 25086, 29024, 33533, 38689, 44579, 51299] 0$6: `Product side is:`, {1, 2, 3, 4, 5, 8, 9, 10, 11, 13, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 37, 38, 39, 40, 41}, `mod `, 42 [1, 1, 2, 3, 5, 7, 10, 13, 19, 25, 34, 44, 58, 75, 96, 122, 155, 194, 243, 302, 375, 462, 567, 693, 845, 1026, 1242, 1497, 1801, 2160, 2584, 3082, 3668, 4354, 5158, 6096, 7190, 8462, 9941, 11655, 13643, 15939, 18593, 21650, 25173, 29223, 33876, 39210, 45324, 52317, 60315] 0$7: `Product side is:`, {1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23}, `mod `, 24 [1, 1, 2, 3, 5, 7, 10, 14, 19, 26, 35, 46, 60, 78, 101, 129, 163, 206, 258, 322, 400, 494, 608, 745, 910, 1107, 1342, 1622, 1955, 2349, 2815, 3364, 4010, 4769, 5659, 6700, 7914, 9331, 10979, 12894, 15115, 17687, 20662, 24097, 28059, 32621, 37867, 43894, 50809, 58732, 67800] #######Family 2.2########### ######Family 2.3########## #####Another##### Prodside(100, {[0$8]}, [{},{[0,0]}, {}],{},[]); `Product side is:`, {1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 22, 23, 24, 25, 26}, `mod `, 27 [1, 1, 2, 2, 4, 5, 8, 10, 15, 19, 27, 34, 46, 58, 77, 97, 126, 157, 200, 248, 313, 385, 480, 587, 726, 883, 1082, 1308, 1592, 1916, 2317, 2775, 3336, 3979, 4758, 5652, 6726, 7959, 9430, 11119, 13122, 15419, 18128, 21233, 24878, 29051, 33927, 39504, 45996, 53412, 62012] ############# Next try [Comp(4,1),Comp(4,1),Comp(4,1)] ################Nandy-Type################# [{[1], [0, 0], [0, 2], [0, 3], [2, 0], [3, 3, 0], [3, 2, 2, 3, 0]},[[2, 2]],[{}, {[0], [1, 0], [3, 0]}],`mod`,12]; `Product side is:`, {1, 4, 6, 8, 11}, `mod `, 12 [1, 1, 1, 1, 2, 2, 3, 3, 5, 5, 6, 7, 10, 11, 13, 14, 19, 21, 25, 28, 35, 38, 45, 50, 62, 68, 79, 87, 104, 115, 133, 147, 173, 190, 217, 240, 279, 307, 348, 383, 440, 484, 546, 601, 683, 749, 840, 923, 1043, 1143, 1275] [[{[1], [0, 0], [0, 2], [0, 3], [2, 0], [3, 3, 0], [3, 2, 2, 3, 0]}, [[1], [2], [3]], [{}, {[0], [1, 3], [3, 0], [3, 2, 3, 0]}], 12], `Product side is:`, {4, 5, 6, 7, 8}, `mod `, 12] [1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 2, 2, 4, 3, 4, 4, 7, 6, 8, 8, 12, 11, 14, 15, 21, 20, 24, 25, 34, 34, 41, 43, 55, 55, 66, 71, 88, 90, 105, 112, 137, 142, 165, 176, 209, 219, 252, 271, 318, 334, 380] [[{[1], [0, 0], [0, 2], [2, 0], [3, 0]}, [[1]], [{}, {[0], [0, 3], [2, 2]}], 12], `Product side is:`, [0, -1, -1, -1, 0, 1, 0, -1, -1, -1, 0, 0]] [1, 0, 1, 1, 2, 1, 2, 2, 4, 3, 5, 5, 8, 7, 10, 10, 15, 14, 19, 20, 27, 26, 34, 36, 47, 47, 59, 63, 79, 81, 99, 106, 130, 135, 162, 174, 208, 219, 258, 278, 328, 347, 404, 436, 507, 540, 621, 671, 772, 825, 941]