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A148517
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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, 1, 0), (1, -1, -1), (1, 0, 0)}
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0
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1, 1, 3, 5, 17, 38, 143, 363, 1408, 3922, 15820, 46805, 191796, 594609, 2486661, 7986637, 33733060, 111492293, 476829005, 1613226513, 6946796857, 23966426413, 104083028616, 365114564090, 1593612887407, 5670563978272, 24903478535676, 89729757443728, 395580997299445, 1440956225867589, 6382522710207952
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..30.
A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
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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, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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
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Sequence in context: A081762 A148515 A148516 * A148518 A077796 A067062
Adjacent sequences: A148514 A148515 A148516 * A148518 A148519 A148520
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers, Nov 18 2008
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STATUS
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approved
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