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A151150
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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), (0, 1, 1), (1, 0, 1), (1, 1, 0)}
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0
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1, 3, 11, 47, 205, 927, 4263, 19873, 93477, 443099, 2111677, 10111271, 48593723, 234274543, 1132435961, 5486484089, 26633535227, 129513967703, 630765345243, 3076177529709, 15020545826403, 73424228430541, 359275730715121, 1759596267979597, 8625046993876771, 42310103527742087, 207699373802231315
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..26.
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, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + 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
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Sequence in context: A151147 A151148 A151149 * A151151 A151152 A151153
Adjacent sequences: A151147 A151148 A151149 * A151151 A151152 A151153
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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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