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Search: id:A148767
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| A148767 |
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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, 1), (-1, 1, 1), (1, 0, -1), (1, 0, 1)} |
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+0
1
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| 1, 1, 3, 7, 29, 93, 365, 1229, 5293, 19663, 83229, 311889, 1387721, 5469539, 23973181, 94601473, 428312559, 1746245251, 7805363683, 31773614049, 145453492511, 606234306813, 2744169647749, 11406695266495, 52617379377691, 222752070436123, 1017257444499731, 4292728234222733, 19913292817906255
(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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A148764 A148765 A148766 this_sequence A151358 A110613 A088095
Adjacent sequences: A148764 A148765 A148766 this_sequence A148768 A148769 A148770
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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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