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A149176
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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, 0, 1), (0, 1, -1), (1, 0, 1)}
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0
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1, 1, 4, 10, 35, 119, 429, 1581, 6038, 23087, 91042, 358768, 1440873, 5803823, 23629737, 96654265, 397874034, 1645654096, 6836257980, 28512765053, 119339831451, 501063355871, 2110078757237, 8908472945971, 37704509580036, 159925254478473, 679736532427123, 2894506638868260, 12347124354033813
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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..28.
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, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A234009 A198324 A149175 * A059710 A149177 A149178
Adjacent sequences: A149173 A149174 A149175 * A149177 A149178 A149179
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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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