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Search: id:A148286
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| A148286 |
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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, -1), (1, 0, 0)} |
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+0
1
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| 1, 1, 2, 5, 12, 35, 101, 305, 998, 3192, 10721, 37044, 126994, 452386, 1619673, 5826276, 21492264, 79114692, 294519731, 1111169430, 4186163252, 15968539928, 61242924850, 235275484768, 913138496950, 3549546890306, 13857948020131, 54467713887561, 214249217663498, 847320663811610, 3363260752897618
(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, k, -1 + n] + aux[i, -1 + j, 1 + 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: A000103 A101292 A131267 this_sequence A075202 A075203 A075205
Adjacent sequences: A148283 A148284 A148285 this_sequence A148287 A148288 A148289
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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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