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A149888
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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, 0), (0, 0, 1), (0, 1, 0), (1, 0, -1)}
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0
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1, 2, 5, 14, 45, 152, 540, 1969, 7418, 28434, 111308, 441236, 1774897, 7205483, 29576110, 122297025, 509955451, 2138900800, 9031575329, 38322118872, 163491504018, 700349095867, 3013663507375, 13013354156399, 56407395819238, 245241519621194, 1069706144537212, 4678214539875211
(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[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A101226 A030126 A149887 * A149889 A149890 A149891
Adjacent sequences: A149885 A149886 A149887 * A149889 A149890 A149891
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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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