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A149583
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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, 0), (0, 0, -1), (1, -1, -1), (1, 1, 1)}
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0
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1, 1, 5, 15, 53, 213, 835, 3295, 13767, 57685, 241077, 1029629, 4454725, 19208365, 83540529, 367533441, 1617265003, 7134065021, 31725845327, 141483149299, 631238921461, 2829861186507, 12734724782627, 57333350858939, 258747925751701, 1171914417315889, 5313618366103365, 24119543507783239
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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..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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A034537 A149581 A149582 * A149584 A147324 A109245
Adjacent sequences: A149580 A149581 A149582 * A149584 A149585 A149586
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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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