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A151250
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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, -1), (0, 1, 1), (1, 0, 1), (1, 1, 0), (1, 1, 1)}
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0
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1, 4, 17, 81, 387, 1882, 9239, 45476, 225097, 1115850, 5543901, 27581511, 137343231, 684560964, 3413759073, 17033098407, 85017930387, 424482793264, 2119935547247, 10589260095977, 52903520205067, 264337253519526, 1320934285008687, 6601511476525466, 32994205139235397, 164914905473037574
(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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 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]]; 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: A089165 A056096 A204326 * A174810 A121545 A078845
Adjacent sequences: A151247 A151248 A151249 * A151251 A151252 A151253
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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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