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Search: id:A149856
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| A149856 |
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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, -1), (-1, -1, 1), (-1, 1, 0), (0, 0, 1), (1, 0, 0)} |
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+0
1
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| 1, 2, 5, 13, 37, 119, 397, 1364, 4718, 16679, 60629, 223411, 831697, 3115490, 11781657, 45056702, 173446087, 671335261, 2610604193, 10205624491, 40127858406, 158396721706, 627451787342, 2493938507817, 9946087760078, 39803742369745, 159716582107213, 642487259246869, 2590943237172682
(list; graph; listen)
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OFFSET
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0,2
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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, j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A119495 A148301 A149855 this_sequence A064384 A148302 A149857
Adjacent sequences: A149853 A149854 A149855 this_sequence A149857 A149858 A149859
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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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