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A148688
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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, 0, 0), (0, -1, 1), (0, 1, 0), (1, -1, 0), (1, 0, -1)}
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0
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1, 1, 3, 7, 22, 69, 232, 812, 2933, 10868, 41176, 158896, 622615, 2473326, 9941501, 40377341, 165508498, 684061812, 2848337029, 11939734114, 50355254586, 213555500201, 910306132464, 3898496289411, 16768128275099, 72411805333357, 313867404311122, 1365162015516800, 5956939958207184
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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[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A035353 A148686 A148687 * A181769 A075214 A070766
Adjacent sequences: A148685 A148686 A148687 * A148689 A148690 A148691
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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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