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A148130
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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, 1), (1, 0, 0), (1, 1, -1)}
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0
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1, 1, 2, 4, 11, 27, 82, 228, 741, 2204, 7439, 23265, 80801, 261285, 925254, 3073545, 11054792, 37460250, 136318642, 469722070, 1726066940, 6026557952, 22317897676, 78816482647, 293824628003, 1047421676406, 3926284015297, 14112557498365, 53156509703810, 192406657606086, 727695258089618, 2650547548516870
(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, j, k, -1 + n] + aux[1 + i, 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: A071314 A123441 A086441 * A131482 A148131 A205504
Adjacent sequences: A148127 A148128 A148129 * A148131 A148132 A148133
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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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