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Search: id:A148806
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| A148806 |
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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, -1, 1), (0, 1, 1), (1, 0, -1)} |
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+0
1
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| 1, 1, 3, 8, 26, 84, 305, 1086, 4078, 15461, 60478, 236475, 944909, 3810840, 15527946, 63575099, 263179621, 1096167860, 4587850961, 19302087093, 81731578479, 347390982785, 1481651268480, 6347010201749, 27296848791921, 117702207650679, 509009215641176, 2208567192496882, 9607641406127315
(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, 1 + k, -1 + n] + aux[i, -1 + 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, 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: A148804 A148805 A000237 this_sequence A148807 A148808 A148809
Adjacent sequences: A148803 A148804 A148805 this_sequence A148807 A148808 A148809
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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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