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A151021
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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, 0), (1, -1, 0), (1, 1, 0), (1, 1, 1)}
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0
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1, 2, 10, 36, 172, 728, 3464, 15568, 74544, 344736, 1661120, 7813024, 37832352, 179948288, 874662336, 4193406912, 20443796032, 98592134144, 481820595712, 2334160892160, 11429701284096, 55569137960192, 272556972992768, 1328958266428416, 6527479856821248, 31903065081293824, 156888633418270720
(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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, j, 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: A001582 A026546 A151020 * A151022 A144895 A154323
Adjacent sequences: A151018 A151019 A151020 * A151022 A151023 A151024
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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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