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A149550
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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), (0, 1, -1), (1, 0, -1), (1, 1, 1)}
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0
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1, 1, 5, 13, 57, 189, 849, 3085, 14289, 54329, 256973, 1007905, 4823589, 19409469, 93423353, 384022225, 1854215189, 7752448757, 37533638481, 158987479205, 771992164281, 3303178546277, 16085325165569, 69393971221993, 338748130781669, 1471878925891841, 7198407214886797, 31477873307999261
(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, j, 1 + k, -1 + n] + aux[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
| Sequence in context: A176648 A159489 A149549 * A149551 A149552 A084136
Adjacent sequences: A149547 A149548 A149549 * A149551 A149552 A149553
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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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