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Search: id:A150943
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| A150943 |
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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, 1), (1, 0, -1), (1, 1, 0), (1, 1, 1)} |
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+0
1
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| 1, 2, 9, 34, 159, 686, 3295, 14981, 72979, 341250, 1675508, 7971231, 39327083, 189258001, 936712081, 4544151795, 22541054385, 109990199579, 546487806524, 2678303694963, 13323363269344, 65516973280506, 326220694997496, 1608413697594238, 8014380398790047, 39597817311750800, 197420514122489922
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
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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, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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
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Sequence in context: A150940 A150941 A150942 this_sequence A150944 A151308 A140217
Adjacent sequences: A150940 A150941 A150942 this_sequence A150944 A150945 A150946
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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