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A148985
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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, 1), (-1, 1, 1), (0, 1, -1), (0, 1, 1), (1, -1, 0)}
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0
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1, 1, 3, 9, 32, 115, 442, 1744, 7051, 29126, 122239, 519591, 2234239, 9694435, 42403432, 186764362, 827508472, 3686022642, 16495984895, 74131461638, 334391209125, 1513451195963, 6870755524144, 31278458876548, 142752688871557, 653025242118420, 2993654192961094, 13750770322469604, 63276530783178980
(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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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
| Sequence in context: A148983 A148984 A194353 * A148986 A052872 A122452
Adjacent sequences: A148982 A148983 A148984 * A148986 A148987 A148988
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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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