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Search: id:A149251
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| A149251 |
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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), (1, 0, -1), (1, 0, 1)} |
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+0
1
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| 1, 1, 4, 11, 38, 135, 535, 1969, 7912, 31803, 131997, 538083, 2286114, 9620153, 41315280, 176490691, 770435360, 3332862297, 14651107025, 64179186301, 284846386574, 1256248612775, 5610121544646, 24960491774219, 112105302989882, 501352545867055, 2263532951079013, 10181662674019503
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
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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[-1 + i, j, 1 + 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
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Sequence in context: A149248 A149249 A149250 this_sequence A149252 A149253 A149254
Adjacent sequences: A149248 A149249 A149250 this_sequence A149252 A149253 A149254
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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