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%I #4 Feb 07 2016 21:41:37
%S 1,4,17,68,270,1064,4181,16404,64322,252184,988890,3879016,15222236,
%T 59764048,234755661,922591156,3627586618,14270426936,56164324206,
%U 221147123768,871147242116,3433076812336,13534723031298,53380361293960,210606884630932
%N Number of North-East paths from (0,0) to (n,n) that have odd number of times bounce off y = x to the right.
%C This sequence is related to paired pattern P_2 in Section 3.2 in Pan and Remmel's link.
%H Ran Pan, Jeffrey B. Remmel, <a href="http://arxiv.org/abs/1601.07988">Paired patterns in lattice paths</a>, arXiv:1601.07988 [math.CO], 2016.
%F a(n) = binomial(2*n,n) - A268430(n).
%F G.f.: (2*x^2)/(1 + f(x) - 2*x*(2 + f(x) + 2*f(x)*x)), where f(x) = sqrt(1 - 4*x).
%Y Cf. A268407, A268429, A268430.
%K nonn
%O 2,2
%A _Ran Pan_, Feb 04 2016
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