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Search: id:A151267
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| A151267 |
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Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 1), (1, -1), (1, 1)} |
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+0
1
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| 1, 1, 3, 7, 21, 55, 165, 457, 1371, 3909, 11727, 33993, 101979, 298629, 895887, 2640931, 7922793, 23460851, 70382553, 209078319, 627234957, 1867531435, 5602594305, 16709292259, 50127876777, 149690954499, 449072863497, 1342297451651, 4026892354953, 12045410486339, 36136231459017, 108154061971965
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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M. Bouquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]
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CROSSREFS
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Sequence in context: A018303 A098545 A161707 this_sequence A091489 A047087 A104779
Adjacent sequences: A151264 A151265 A151266 this_sequence A151268 A151269 A151270
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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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