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A149534
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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, -1), (0, -1, 0), (1, -1, 0), (1, 1, 1)}
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0
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1, 1, 5, 13, 49, 177, 667, 2511, 10009, 39187, 155965, 634409, 2572311, 10467813, 43375789, 178967139, 740636461, 3103154817, 12965474087, 54264996479, 229254996155, 966417702403, 4079049705641, 17340341569785, 73594562906139, 312632789194025, 1335568546118335, 5698403070572647
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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, k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, 1 + 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: A084601 A149532 A149533 * A149535 A149536 A149537
Adjacent sequences: A149531 A149532 A149533 * A149535 A149536 A149537
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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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