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%I #9 Sep 08 2019 02:26:03
%S 0,1,4,14,52,195,728,2716,10136,37829,141180,526890,1966380,7338631,
%T 27388144,102213944,381467632,1423656585,5313158708,19828978246,
%U 74002754276,276182038859,1030725401160,3846719565780,14356152861960
%N Expansion of x/((1 + x^2)*(1 - 4*x + x^2)).
%C A Chebyshev transform of the sequence 0,1,4,16,... which has g.f. x/(1-4x). The image of G(x) under the Chebyshev transform is (1/(1+x^2))*G(x/(1+x^2)).
%F G.f.: x/((1 + x^2)*(1 - 4*x + x^2)).
%F a(n) = 4*a(n-1) - 2*a(n-2) + 4*a(n-3).
%F a(n) = Sum_{k=0..n} cos(Pi*(n-k)/2)*((2+sqrt(3))^k - (2-sqrt(3))^k)/(2*sqrt(3)).
%F a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)*(-1)^n*(4^(n-2*k) - 0^(n-2*k))/4.
%Y Cf. A099487, A099488.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Oct 18 2004
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