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%I #8 Oct 06 2018 11:43:31
%S 1,6,31,146,655,2850,12148,51028,212039,873870,3578404,14578576,
%T 59149381,239177006,964439355,3879856458,15577609711,62439489346,
%U 249917575553,999080441830,3989726087031,15917901326330,63457122234055,252796365476922,1006456231070795,4004838954237250,15928299669867291
%N 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 This sequence is related to paired pattern P_2 in Pan and Remmel's link.
%C 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 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 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 Cf. A268400.
%K nonn
%O 4,2
%A _Ran Pan_, Feb 03 2016
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