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 A268401 #8 Oct 06 2018 11:43:31 %S A268401 1,6,31,146,655,2850,12148,51028,212039,873870,3578404,14578576, %T A268401 59149381,239177006,964439355,3879856458,15577609711,62439489346, %U A268401 249917575553,999080441830,3989726087031,15917901326330,63457122234055,252796365476922,1006456231070795,4004838954237250,15928299669867291 %N A268401 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. %C A268401 This sequence is related to paired pattern P_2 in Pan and Remmel's link. %C A268401 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. %H A268401 Ran Pan and Jeffrey B. Remmel, <a href="http://arxiv.org/abs/1601.07988">Paired patterns in lattice paths</a>, arXiv:1601.07988 [math.CO], 2016. %F A268401 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). %Y A268401 Cf. A268400. %K A268401 nonn %O A268401 4,2 %A A268401 _Ran Pan_, Feb 03 2016