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A149887
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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, 0, 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, 535, 1943, 7289, 27876, 108448, 428477, 1716434, 6947541, 28393225, 117079643, 486515806, 2034989189, 8565051207, 36256323523, 154246683731, 659219337990, 2829613175204, 12193980235432, 52737388566862, 228850945637483, 996246088634899, 4349589171641900
(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, 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: A134378 A101226 A030126 * A149888 A149889 A149890
Adjacent sequences: A149884 A149885 A149886 * A149888 A149889 A149890
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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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