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A148038
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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, 0), (0, 0, -1), (0, 1, -1), (1, 0, 0)}
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1, 1, 2, 3, 8, 19, 53, 150, 435, 1373, 4234, 13803, 45615, 152565, 525436, 1807917, 6370454, 22648924, 81045274, 294605006, 1074167523, 3960848064, 14708826191, 54866285401, 206578823690, 780529431496, 2967546723380, 11346226883771, 43526990900201, 167962909112062, 650320995547081, 2527858507702086
(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, -1 + 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, -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: A100342 A041281 A078343 * A148039 A148040 A148041
Adjacent sequences: A148035 A148036 A148037 * A148039 A148040 A148041
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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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