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A150387
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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, 0), (-1, 1, 1), (1, 0, 1), (1, 1, 0)}
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0
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1, 2, 7, 23, 100, 368, 1710, 6716, 31823, 130061, 623003, 2611508, 12616721, 53820289, 261699739, 1131097502, 5525211564, 24129146559, 118255755796, 520778209686, 2558745315274, 11346116005601, 55860667523716, 249129364575265, 1228616735554889, 5506312402878732, 27193271314477361, 122388911479518502
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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
| Sequence in context: A150384 A150385 A150386 * A150388 A073344 A038119
Adjacent sequences: A150384 A150385 A150386 * A150388 A150389 A150390
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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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