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A151134
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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), (0, 1, -1), (0, 1, 0), (1, 0, 1), (1, 1, 0)}
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0
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1, 3, 11, 46, 199, 886, 4041, 18650, 87067, 409948, 1942194, 9252987, 44275380, 212631652, 1024425845, 4948669739, 23961382923, 116258790149, 565088984403, 2751081693868, 13412495030899, 65474358544596, 319989821978886, 1565512729578621, 7666415523836689, 37575804568154351, 184320223962376524
(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[i, -1 + j, k, -1 + n] + aux[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: A030889 A030854 A027135 * A151135 A151136 A151137
Adjacent sequences: A151131 A151132 A151133 * A151135 A151136 A151137
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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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