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A149929
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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, 1, -1), (0, 0, 1), (0, 1, -1), (1, 0, 0)}
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0
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1, 2, 5, 15, 48, 168, 608, 2268, 8662, 33778, 134184, 539871, 2197090, 9030000, 37459341, 156606474, 659061461, 2790192515, 11877890745, 50819264437, 218390536236, 942266919891, 4080623902277, 17732994440363, 77305062398569, 337974770301276, 1481583893527512, 6511260259152370
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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..27.
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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A006570 A149928 A003430 * A149930 A189924 A190908
Adjacent sequences: A149926 A149927 A149928 * A149930 A149931 A149932
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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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