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Search: id:A148443
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| A148443 |
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Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, -1, 1), (-1, 0, 0), (0, 0, 1), (1, 1, -1)} |
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+0
1
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| 1, 1, 2, 6, 16, 47, 157, 507, 1714, 6074, 21360, 77241, 284811, 1051900, 3954103, 15003471, 57201331, 220534963, 855038657, 3332650936, 13084082094, 51582007825, 204327262149, 813393343533, 3249188679150, 13031012456908, 52450320596046, 211746189564692, 857602778653967, 3483222763555429
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
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aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
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CROSSREFS
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Sequence in context: A003291 A148442 A071726 this_sequence A148444 A064190 A151281
Adjacent sequences: A148440 A148441 A148442 this_sequence A148444 A148445 A148446
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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