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A149121
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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, 1, -1), (1, -1, 0), (1, 1, 1)}
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0
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1, 1, 4, 9, 34, 94, 368, 1131, 4398, 14236, 55984, 188576, 740000, 2551442, 10067316, 35443271, 139712062, 498416468, 1971107420, 7122847862, 28153558524, 102603939062, 406431688608, 1494188962016, 5916706122284, 21880889654074, 86779037261076, 322951842854822, 1280521402780940, 4786287052515392
(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, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A173659 A054433 A096531 * A149122 A149123 A149124
Adjacent sequences: A149118 A149119 A149120 * A149122 A149123 A149124
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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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