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A149433
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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), (1, -1, 0), (1, 1, -1), (1, 1, 1)}
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0
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1, 1, 4, 13, 46, 160, 590, 2165, 8150, 30606, 116538, 443508, 1702458, 6538806, 25255218, 97606497, 378655122, 1470166114, 5723589574, 22300607746, 87061280866, 340147775826, 1330975341918, 5211699279580, 20431613875778, 80150459987066, 314718467976066, 1236491484795006, 4861807577614986
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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[-1 + 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: A320743 A104460 A095128 * A047154 A180144 A149434
Adjacent sequences: A149430 A149431 A149432 * A149434 A149435 A149436
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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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