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A149428
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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, 0), (1, 1, -1), (1, 1, 1)}
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0
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1, 1, 4, 13, 44, 156, 560, 2049, 7684, 28772, 108368, 412396, 1573776, 6029488, 23226176, 89573577, 346281380, 1343190436, 5216949776, 20296197484, 79131832976, 308798743728, 1206495306816, 4720960267204, 18487515792272, 72463886990864, 284340829780288, 1116404838166192, 4386449721693760
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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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, 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: A252933 A229397 A283110 * A149429 A045652 A149430
Adjacent sequences: A149425 A149426 A149427 * A149429 A149430 A149431
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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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