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Search: id:A148303
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| A148303 |
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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, 1), (-1, 0, 1), (0, 1, -1), (1, 0, -1), (1, 0, 0)} |
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+0
1
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| 1, 1, 2, 5, 13, 38, 119, 392, 1322, 4723, 17050, 63318, 241270, 927321, 3646707, 14487316, 58273122, 237345018, 974596819, 4042834966, 16899686492, 71177203798, 301888303055, 1288368101304, 5531248745963, 23874467843991, 103578452298336, 451465919599721, 1976580424093861, 8689421522149543
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A149857 A001475 A149858 this_sequence A148304 A149859 A000800
Adjacent sequences: A148300 A148301 A148302 this_sequence A148304 A148305 A148306
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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