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A149826
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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, 0, 0), (0, 0, 1), (0, 1, 0), (1, -1, -1)}
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0
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1, 2, 4, 10, 28, 85, 275, 924, 3161, 11123, 40356, 148994, 555317, 2099039, 8057473, 31247345, 122019881, 480549169, 1909455313, 7638161881, 30713415080, 124209720711, 505237712256, 2064851613757, 8472358195113, 34907360687287, 144413933270171, 599556168765568, 2496836471032115
(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[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A192574 A135336 A149825 * A149827 A149828 A149829
Adjacent sequences: A149823 A149824 A149825 * A149827 A149828 A149829
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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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