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A148110
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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, 0, 0), (0, -1, 1), (0, 1, 0), (1, 0, -1)}
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0
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1, 1, 2, 4, 10, 28, 82, 255, 817, 2736, 9364, 32887, 117702, 429126, 1588138, 5956905, 22619993, 86823782, 336549149, 1316036640, 5188377504, 20605943013, 82394676296, 331529401307, 1341732208261, 5459350403375, 22324604170221, 91717955898433, 378460253610202, 1568052594398459, 6521808096528806
(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, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A034472 A094388 A187256 * A149823 A192653 A149824
Adjacent sequences: A148107 A148108 A148109 * A148111 A148112 A148113
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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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