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A148843
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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, 1), (-1, 1, 0), (0, 1, -1), (1, 0, 1)}
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0
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1, 1, 3, 8, 27, 95, 318, 1216, 4572, 17233, 67516, 267865, 1059018, 4251626, 17287544, 70360191, 287710744, 1188208755, 4923026388, 20420750812, 85249374158, 357241170401, 1498609977327, 6308007595953, 26650792606933, 112732684078032, 477768163407118, 2030664845038008, 8644272087548518
(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, -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, 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: A000238 A148841 A148842 * A148844 A145760 A102318
Adjacent sequences: A148840 A148841 A148842 * A148844 A148845 A148846
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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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