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A150908
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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, 1, -1), (0, 0, -1), (1, 0, 1), (1, 1, 1)}
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0
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1, 2, 9, 31, 143, 592, 2698, 12137, 55724, 258672, 1206963, 5675883, 26848465, 127379555, 607671354, 2905444843, 13938687704, 67042101669, 323124345956, 1560836312434, 7552502276302, 36604439669343, 177681390928731, 863603611066566, 4202731264776623, 20475730877063532, 99860486183124377
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..26.
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, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A150905 A150906 A150907 * A150909 A150910 A150911
Adjacent sequences: A150905 A150906 A150907 * A150909 A150910 A150911
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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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