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Search: id:A150563
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| A150563 |
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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, 0, 1), (0, 1, 1), (1, -1, 1), (1, 0, -1)} |
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+0
1
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| 1, 2, 7, 26, 107, 454, 1993, 8925, 40635, 187211, 871038, 4084109, 19272792, 91434267, 435748119, 2084649727, 10006344868, 48169762525, 232474453125, 1124473288678, 5449894396391, 26460614817603, 128678573324734, 626670841164169, 3055913760675905, 14919699190585789, 72920857849558325
(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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 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: A150561 A122871 A150562 this_sequence A150564 A150565 A150566
Adjacent sequences: A150560 A150561 A150562 this_sequence A150564 A150565 A150566
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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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