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Search: id:A151323
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| A151323 |
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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, 0), (0, -1), (0, 1), (1, 0), (1, 1)} |
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+0
1
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| 1, 3, 14, 67, 342, 1790, 9580, 52035, 285990, 1586298, 8864676, 49844238, 281719164, 1599314652, 9113895960, 52109150691, 298806189318, 1717855010274, 9898828072692, 57158263594458, 330662400729492, 1916134078427556, 11120825740970088, 64634042348169294, 376139362185133404, 2191569966890629380
(list; graph; listen)
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OFFSET
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0,2
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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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FORMULA
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G.f. appears to be (((1+2*x)/(1-6*x))^(1/4)-1)/(2*x) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Nov 20 2009]
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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, j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, 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: A034275 A151322 A002320 this_sequence A113140 A151324 A121185
Adjacent sequences: A151320 A151321 A151322 this_sequence A151324 A151325 A151326
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KEYWORD
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nonn,walk,new
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AUTHOR
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Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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