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A148305
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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, 0, 0), (-1, 0, 1), (0, 1, 0), (1, -1, 0), (1, 1, -1)}
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0
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1, 1, 2, 5, 13, 39, 127, 425, 1508, 5564, 20962, 81250, 322242, 1298027, 5313358, 22075715, 92778080, 394026108, 1690459141, 7315000807, 31892994079, 140059021519, 619096017277, 2752326799850, 12302159156136, 55264374463007, 249388391938448, 1130125080446317, 5141521020955342
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
| 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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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
| Sequence in context: A151446 A022894 A149861 * A104447 A127986 A133448
Adjacent sequences: A148302 A148303 A148304 * A148306 A148307 A148308
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KEYWORD
| nonn,walk
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AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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