This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A268431 #4 Feb 07 2016 21:41:37 %S A268431 1,4,17,68,270,1064,4181,16404,64322,252184,988890,3879016,15222236, %T A268431 59764048,234755661,922591156,3627586618,14270426936,56164324206, %U A268431 221147123768,871147242116,3433076812336,13534723031298,53380361293960,210606884630932 %N A268431 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 A268431 This sequence is related to paired pattern P_2 in Section 3.2 in Pan and Remmel's link. %H A268431 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 A268431 a(n) = binomial(2*n,n) - A268430(n). %F A268431 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 A268431 Cf. A268407, A268429, A268430. %K A268431 nonn %O A268431 2,2 %A A268431 _Ran Pan_, Feb 04 2016