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Search: id:A148842
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| A148842 |
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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, -1, 1), (0, 1, 0), (1, -1, 1), (1, 0, -1)} |
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+0
1
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| 1, 1, 3, 8, 27, 93, 341, 1295, 5052, 20209, 82190, 339801, 1422276, 6020724, 25727971, 110854465, 481147223, 2101771068, 9234216691, 40779355432, 180925623756, 806086402420, 3605151047127, 16180065798799, 72849331715413, 328964096764340, 1489531226709228, 6761473239089773, 30764122078267794
(list; graph; listen)
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OFFSET
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0,3
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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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + 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
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Sequence in context: A047153 A000238 A148841 this_sequence A148843 A148844 A145760
Adjacent sequences: A148839 A148840 A148841 this_sequence A148843 A148844 A148845
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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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