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Search: id:A149815
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| A149815 |
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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, -1), (0, 0, 1), (0, 1, 0), (1, -1, -1)} |
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+0
1
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| 1, 2, 4, 10, 26, 76, 248, 796, 2654, 8942, 30952, 112110, 403446, 1474050, 5415092, 20126040, 76723180, 291325720, 1115293334, 4283685580, 16561655330, 65111198066, 255211841296, 1005521776936, 3970064457452, 15742010094734, 63185813520174, 252973809922464, 1016451149145374, 4089942429478792
(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[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 1 + 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: A000085 A047653 A148100 this_sequence A149816 A149817 A149818
Adjacent sequences: A149812 A149813 A149814 this_sequence A149816 A149817 A149818
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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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