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A150629
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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), (0, 1, 1), (1, 0, -1), (1, 0, 1)}
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0
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1, 2, 7, 27, 115, 494, 2199, 9999, 45977, 213553, 1001518, 4728343, 22440120, 106995630, 512350724, 2461339951, 11857180503, 57274958341, 277281579581, 1344921183407, 6535047490259, 31805222581625, 155007158817484, 756405069981852, 3695465159418088, 18073604576901871, 88477876035516269
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[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
| Sequence in context: A180473 A154108 A011965 * A150630 A150631 A150632
Adjacent sequences: A150626 A150627 A150628 * A150630 A150631 A150632
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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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