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Search: id:A149303
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| A149303 |
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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, 1, 1), (0, 0, -1), (1, -1, 1), (1, 1, 0)} |
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+0
1
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| 1, 1, 4, 11, 46, 174, 740, 3109, 13614, 59878, 268728, 1214032, 5546558, 25498422, 118054700, 549367029, 2569472992, 12066493332, 56883907318, 269035738044, 1276275732442, 6070582701920, 28945492531456, 138319277521604, 662316708110916, 3177211680848070, 15267484859916084, 73479492803233664
(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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A149300 A149301 A149302 this_sequence A053882 A149304 A149305
Adjacent sequences: A149300 A149301 A149302 this_sequence A149304 A149305 A149306
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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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