%I #5 Feb 03 2016 16:45:43
%S 5,24,95,356,1309,4784,17472,63920,234498,863056,3187041,11807740,
%T 43885725,163601760,611625660,2292665760,8615485590,32451382800,
%U 122499978510,463369822344,1756113365874,6667436894624,25357090075600,96589604043296,368478056090340,1407687015207200,5384924914890213
%N Number of North-East lattice paths from (0,0) to (n,n) that have exactly three east steps below the subdiagonal y = x-1.
%C This sequence is related to paired pattern P_1 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 G.f.: -((-1 + f(x) + 2*x)^2*(-1 + f(x) + 2*(f(x) - 2*x)*x))/(8*x^2), where f(x) = sqrt(1 - 4*x).
%Y Cf. A120989, A002057, A000108.
%K nonn
%O 4,1
%A _Ran Pan_, Feb 03 2016
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