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A148086
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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)}
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0
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1, 1, 2, 4, 10, 22, 59, 149, 396, 1041, 2907, 7760, 21816, 60298, 169741, 475054, 1359128, 3816950, 10972685, 31304334, 89879700, 257711500, 747124581, 2144777317, 6229523512, 18035524556, 52361269786, 152014079572, 443837403206, 1288731108002, 3768163857728, 11001149176426, 32145852887328
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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, 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: A030234 A205490 A205499 * A179468 A203254 A076875
Adjacent sequences: A148083 A148084 A148085 * A148087 A148088 A148089
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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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