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A148015
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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), (0, 0, -1), (1, 0, 0)}
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0
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1, 1, 2, 3, 8, 17, 46, 110, 335, 932, 2810, 7952, 24816, 77649, 246474, 775403, 2494697, 8205868, 27285758, 89808549, 299916394, 1015055715, 3470516713, 11875011937, 40535085083, 140299654185, 489869705096, 1712127093499, 5997291296577, 21043269839009, 74602647699984, 265584478448207, 944077259383298
(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, j, k, -1 + n] + aux[i, j, 1 + 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
| Sequence in context: A182889 A099965 A148014 * A148016 A148017 A148018
Adjacent sequences: A148012 A148013 A148014 * A148016 A148017 A148018
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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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