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Search: id:A150994
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| A150994 |
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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), (0, -1, 1), (1, 0, -1), (1, 1, 0), (1, 1, 1)} |
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+0
1
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| 1, 2, 9, 38, 170, 788, 3701, 17621, 84743, 409854, 1993846, 9739235, 47723741, 234520717, 1154955011, 5698424753, 28160079693, 139341098410, 690273126559, 3422846851125, 16987118264372, 84367242024066, 419283901941142, 2084919612584816, 10372633738439073, 51627625733592623, 257067798731839391
(list; graph; listen)
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OFFSET
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0,2
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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[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 1 + 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: A037569 A001077 A150993 this_sequence A150995 A150996 A150997
Adjacent sequences: A150991 A150992 A150993 this_sequence A150995 A150996 A150997
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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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