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Search: id:A148915
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| A148915 |
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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, 1, -1), (0, 1, 1), (1, -1, 1)} |
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+0
1
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| 1, 1, 3, 8, 32, 110, 444, 1676, 7090, 28314, 121990, 504920, 2212372, 9382416, 41584876, 179539056, 803135830, 3514731918, 15837959224, 70054928916, 317581225854, 1416879893330, 6455464123356, 29006054220056, 132718076206868, 599896260799838, 2754895622501684, 12515550063373760, 57657852586593046
(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, -1 + 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: A148912 A148913 A148914 this_sequence A151541 A022563 A103939
Adjacent sequences: A148912 A148913 A148914 this_sequence A148916 A148917 A148918
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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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