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Search: id:A149431
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| A149431 |
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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, 0, 0), (-1, 0, 1), (0, -1, 1), (0, 0, -1), (1, 1, 0)} |
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+0
1
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| 1, 1, 4, 13, 45, 171, 689, 2756, 11351, 47976, 204381, 878826, 3824025, 16776688, 74021638, 328681019, 1467532698, 6581442360, 29637099404, 133969162219, 607582367783, 2763746150889, 12606655549991, 57648997909311, 264223264007648, 1213578131312042, 5584897636305793, 25748047536912449
(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, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A005490 A035356 A165205 this_sequence A149432 A155397 A155328
Adjacent sequences: A149428 A149429 A149430 this_sequence A149432 A149433 A149434
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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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