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A151253
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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), (0, 0, 1), (1, 0, 0), (1, 0, 1), (1, 1, 0)}
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1
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1, 4, 19, 91, 445, 2188, 10819, 53644, 266581, 1326646, 6609307, 32953033, 164397313, 820521562, 4096733707, 20459928259, 102203137741, 510621146326, 2551485015379, 12750737780587, 63725988599425, 318514790389294, 1592093707211299, 7958459733327676, 39783873348471745, 198883941062337328
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A151162 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 03 2009]
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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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[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: A010907 A087449 A004253 * A121179 A131552 A122369
Adjacent sequences: A151250 A151251 A151252 * A151254 A151255 A151256
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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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