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Search: id:A148370
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| A148370 |
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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, 0, 1), (-1, 1, -1), (0, 1, 1), (1, 0, -1)} |
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+0
1
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| 1, 1, 2, 5, 16, 42, 147, 454, 1628, 5425, 20178, 70153, 268235, 963094, 3750168, 13820410, 54545612, 205188861, 818752204, 3130596415, 12607433542, 48850200688, 198265158766, 776800033465, 3173598172091, 12552548689917, 51573263660315, 205664370031343, 849144348277944, 3410421662866518
(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[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A102866 A148368 A148369 this_sequence A148371 A148372 A148373
Adjacent sequences: A148367 A148368 A148369 this_sequence A148371 A148372 A148373
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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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