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A151063
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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), (0, 0, 1), (0, 1, 0), (1, 0, 0), (1, 1, -1)}
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0
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1, 3, 10, 38, 158, 685, 3059, 13975, 64874, 304870, 1446786, 6918827, 33293647, 161031214, 782158641, 3812561357, 18639652369, 91361676115, 448784432997, 2208659743464, 10887516009780, 53746103987151, 265648123726347, 1314446849434601, 6510288532121706, 32272353420424580, 160100626261021076
(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, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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
| Sequence in context: A001002 A151062 A000902 * A103138 A074527 A186367
Adjacent sequences: A151060 A151061 A151062 * A151064 A151065 A151066
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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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