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A149271
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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, 0, 0), (-1, 0, 1), (1, -1, 0), (1, 1, 0)}
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0
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1, 1, 4, 11, 42, 131, 561, 1897, 8264, 30205, 133945, 505237, 2280622, 8858735, 40332662, 160335565, 735744074, 2972238961, 13729284799, 56239449957, 261023413798, 1081746128971, 5041413026620, 21089879774557, 98638353015282, 416028438965419, 1951434704818877, 8289421176613483
(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[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A000296 A032265 A151273 * A149272 A149273 A149274
Adjacent sequences: A149268 A149269 A149270 * A149272 A149273 A149274
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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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