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%I #6 Jun 13 2015 00:51:33
%S 1,1,3,14,53,195,727,2716,10137,37829,141179,526890,1966381,7338631,
%T 27388143,102213944,381467633,1423656585,5313158707,19828978246,
%U 74002754277,276182038859,1030725401159,3846719565780,14356152861961
%N Expansion of (1-3x+x^2)/((1+x^2)(1-4x+x^2)).
%C A Chebyshev transform of the sequence 1,1,4,16.. which has with g.f. (1-3x)/(1-4x). The image of G(x) under the Chebyshev transform is (1/(1+x^2))G(x/(1+x^2)).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,4,-1).
%F a(n)=4a(n-1)-2a(n-2)+4a(n-3); a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^n*(4^(n-2k)+3*0^(n-2k))/4}.
%Y Cf. A099486, A099488.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Oct 18 2004
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