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Search: id:A148169
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| A148169 |
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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, 1, 1), (0, 0, 1), (0, 1, -1), (1, -1, 1)} |
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+0
1
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| 1, 1, 2, 4, 11, 31, 103, 342, 1223, 4392, 16506, 62556, 244133, 960293, 3851560, 15555730, 63698508, 262461123, 1092521898, 4572692026, 19288640555, 81754788980, 348654622331, 1493144372062, 6426427761938, 27761268531353, 120419760141811, 524043699721912, 2288472222005169, 10022411092677579
(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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + 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, -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: A148167 A148168 A004251 this_sequence A110140 A115625 A056323
Adjacent sequences: A148166 A148167 A148168 this_sequence A148170 A148171 A148172
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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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