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A148928
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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, 0), (0, -1, 1), (0, 1, -1), (1, 0, 1)}
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0
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1, 1, 3, 9, 27, 97, 343, 1257, 4838, 18667, 73563, 296072, 1196444, 4906843, 20317977, 84581199, 355455832, 1502010343, 6379990024, 27262864080, 116966557176, 503988871237, 2180480955718, 9464214424929, 41218477076464, 180054523886628, 788636805693075, 3463448527252381, 15246364612110953
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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, 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, 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: A148926 A146573 A148927 * A029527 A148929 A148930
Adjacent sequences: A148925 A148926 A148927 * A148929 A148930 A148931
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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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