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A150399
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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, 1, 0), (0, 0, 1), (1, 0, -1), (1, 0, 1)}
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0
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1, 2, 7, 24, 92, 365, 1526, 6468, 28070, 123328, 551027, 2481736, 11293654, 51699421, 238494777, 1105386224, 5152893766, 24107334035, 113276230772, 533854758783, 2524939255462, 11971164315644, 56917304205885, 271169952254866, 1294984275269412, 6195065421673464, 29694797256528747, 142549284282691133
(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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150396 A150397 A150398 * A150400 A150401 A003041
Adjacent sequences: A150396 A150397 A150398 * A150400 A150401 A150402
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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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