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A150050
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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), (0, 0, -1), (0, 0, 1), (0, 1, -1), (1, 0, 0)}
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0
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1, 2, 6, 18, 61, 216, 805, 3106, 12273, 49713, 204584, 856073, 3627081, 15541148, 67265699, 293557472, 1291371759, 5718657166, 25482111083, 114180541557, 514173146013, 2326225644455, 10568079142209, 48198378627602, 220604026242275, 1013030819655013, 4666248466740808, 21554720609186250
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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[i, 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: A150047 A150048 A150049 * A192318 A192483 A150051
Adjacent sequences: A150047 A150048 A150049 * A150051 A150052 A150053
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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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