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A149801
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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, 1), (-1, 1, 0), (1, -1, 0), (1, 1, -1), (1, 1, 1)}
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0
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1, 1, 5, 19, 89, 375, 1803, 8099, 39461, 183163, 899665, 4260553, 21031851, 100905983, 499745741, 2419272721, 12008569813, 58509307135, 290886878755, 1424079548509, 7088274898263, 34828332807003, 173507891245677, 854954241419145, 4262067131854465, 21048441297994881, 104984134357373563
(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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A147099 A154598 A184513 * A149802 A149803 A149804
Adjacent sequences: A149798 A149799 A149800 * A149802 A149803 A149804
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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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