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A150755
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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), (-1, 1, 0), (1, 0, -1), (1, 0, 1), (1, 1, 0)}
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0
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1, 2, 8, 29, 129, 541, 2525, 11276, 53863, 248774, 1204571, 5679910, 27736565, 132586989, 651147483, 3142500414, 15494753033, 75299549782, 372356453623, 1818954191751, 9014184000438, 44209968536973, 219452435722788, 1079666387779406, 5366184367875090, 26466342989496672, 131676516017179361
(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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A162066 A151302 A150754 * A150756 A150757 A150758
Adjacent sequences: A150752 A150753 A150754 * A150756 A150757 A150758
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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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