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A148785
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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, 0, 0), (0, 0, 1), (1, 0, -1), (1, 1, -1)}
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0
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1, 1, 3, 8, 24, 79, 272, 952, 3489, 13099, 49492, 191991, 756217, 2987651, 12009132, 48784729, 198487593, 817580395, 3394076108, 14101066526, 59132483007, 249475228049, 1052861357844, 4476155320845, 19122462766588, 81696336981114, 351123564811666, 1515127482420775, 6537005619601408
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
| 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[-1 + i, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 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
| Sequence in context: A118099 A066350 A148784 * A148786 A088966 A148787
Adjacent sequences: A148782 A148783 A148784 * A148786 A148787 A148788
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KEYWORD
| nonn,walk
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AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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