Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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