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A151235
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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, 0, 0), (1, 0, 0), (1, 1, 0), (1, 1, 1)}
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0
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1, 3, 14, 59, 286, 1302, 6396, 30093, 148762, 712466, 3534356, 17112094, 85071796, 414867684, 2065425648, 10123488801, 50449616658, 248190199130, 1237712225980, 6106027045386, 30466402339948, 150625539734428, 751853521099392, 3723506571470266, 18591722017819844, 92200733893743892
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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[-1 + i, j, k, -1 + n] + aux[1 + i, j, 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
| Sequence in context: A126875 A110526 A038679 * A151236 A006224 A131262
Adjacent sequences: A151232 A151233 A151234 * A151236 A151237 A151238
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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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