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A149361
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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, 0, 1), (0, -1, 1), (0, 1, -1), (1, 0, 1)}
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0
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1, 1, 4, 12, 44, 159, 639, 2483, 10352, 42294, 180524, 759732, 3300850, 14177275, 62395356, 272032994, 1209154365, 5332085353, 23887620632, 106288427057, 479225640782, 2147863892316, 9735742908666, 43897759860785, 199873733602718, 905778443184985, 4140076800330287, 18842880038050095
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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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A060897 A005190 A149360 * A149362 A149363 A188632
Adjacent sequences: A149358 A149359 A149360 * A149362 A149363 A149364
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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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