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Search: id:A149757
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| A149757 |
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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), (1, -1, 1), (1, 1, -1), (1, 1, 1)} |
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+0
1
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| 1, 1, 5, 17, 85, 343, 1715, 7501, 37505, 171085, 855425, 3999601, 19998005, 94992091, 474960455, 2280616019, 11403080095, 55180159045, 275900795225, 1342819665229, 6714098326145, 32822357011259, 164111785056295, 805053179115385, 4025265895576925, 19800669173042077, 99003345865210385
(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[-1 + 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] + 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: A038183 A149756 A036756 this_sequence A153499 A012782 A026685
Adjacent sequences: A149754 A149755 A149756 this_sequence A149758 A149759 A149760
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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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