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A148094
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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), (0, 1, -1), (1, -1, 0)}
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0
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1, 1, 2, 4, 10, 25, 75, 217, 686, 2136, 7143, 23473, 81750, 280112, 1000476, 3529443, 12926899, 46740449, 174248545, 642573826, 2432741851, 9116884251, 34979496027, 132930156161, 515588023612, 1982470289972, 7765603476152, 30166998260556, 119166643516657, 467106203960011, 1859074152674149
(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, 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: A152958 A148093 A206289 * A148095 A124419 A148096
Adjacent sequences: A148091 A148092 A148093 * A148095 A148096 A148097
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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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