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Search: id:A147999
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| A147999 |
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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, 0), (1, 0, 0)} |
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+0
2
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| 1, 1, 2, 3, 8, 15, 39, 77, 244, 543, 1655, 3729, 12385, 29510, 93170, 221283, 764948, 1908675, 6323115, 15688889, 55069789, 141067986, 473165330, 1200395415, 4290381497, 11232104990, 38585190644, 100082744787, 360316046969, 956558534943, 3305432502421, 8679121868177, 31575545872868, 84905308145331
(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[1 + i, -1 + j, 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: A055543 A049957 A151255 this_sequence A148000 A148001 A148002
Adjacent sequences: A147996 A147997 A147998 this_sequence A148000 A148001 A148002
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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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