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A148300
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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, 1, 0), (-1, 1, 1), (0, 0, 1), (1, 0, -1)}
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0
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1, 1, 2, 5, 13, 36, 117, 376, 1268, 4416, 15530, 56200, 206917, 771777, 2918347, 11132217, 42902292, 166855034, 653846383, 2580452228, 10243450403, 40893533547, 164120740217, 661823233025, 2680586062806, 10899832075916, 44484624408459, 182181730745624, 748510944968676, 3084555328960212
(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, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + 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]]; 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: A148297 A148298 A148299 * A038982 A019415 A175118
Adjacent sequences: A148297 A148298 A148299 * A148301 A148302 A148303
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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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