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A268401
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Number of North-East lattice paths from (0,0) to (n,n) that bounce off the diagonal y = x to the right exactly three times.
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1
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1, 6, 31, 146, 655, 2850, 12148, 51028, 212039, 873870, 3578404, 14578576, 59149381, 239177006, 964439355, 3879856458, 15577609711, 62439489346, 249917575553, 999080441830, 3989726087031, 15917901326330, 63457122234055, 252796365476922, 1006456231070795, 4004838954237250, 15928299669867291
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OFFSET
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4,2
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COMMENTS
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This sequence is related to paired pattern P_2 in Pan and Remmel's link.
By symmetry, it is also the number of North-East lattice paths from (0,0) to (n,n) that bounce off the diagonal y = x to the left exactly three times.
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LINKS
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FORMULA
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G.f.: -((-1 + f(x))^4*x^2*(-1 + f(x) + 2*x))/(2*(1 - f(x) + (-5 + f(x))*x)^4), where f(x) = sqrt(1 - 4*x).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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