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Search: id:A151255
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| A151255 |
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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, 0)} |
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+0
1
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| 1, 1, 2, 3, 8, 15, 39, 77, 216, 459, 1265, 2739, 7842, 17641, 49854, 113175, 327604, 761787, 2182833, 5101595, 14868582, 35338401, 102146176, 243510453, 713019480, 1721265625, 5005198029, 12105626337, 35565979706, 86870058279, 253706973975, 620415879229, 1827423157812, 4504531840875, 13199126952109
(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.
M. Bouquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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FORMULA
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G.f. 1/4*(-2*x+1)/x^2*(1-((x+1)/(1-3*x))^(1/2)*(1-2*Int(((8*x^2+1)*(1+4*x)*(2*x^2-4*x+1)*hypergeom([1/4, 3/4],[1],64*x^4)+12*(8*x^2+1)*x^3*(8*x^2-1)*(1-7*x+4*x^2)*hypergeom([5/4, 7/4],[2],64*x^4))/(1-3*x)^(1/2)/(-1+2*x)^2/(x+1)^(3/2),x))) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Oct 13 2009] [Needs to be written avoiding the a/b/c/d... notation! - N. J. A. Slaone, Oct 15 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, 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: A132862 A055543 A049957 this_sequence A147999 A148000 A148001
Adjacent sequences: A151252 A151253 A151254 this_sequence A151256 A151257 A151258
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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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