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 A099488 #8 Jun 23 2015 09:40:22
%S A099488 1,2,7,28,105,390,1455,5432,20273,75658,282359,1053780,3932761,
%T A099488 14677262,54776287,204427888,762935265,2847313170,10626317415,
%U A099488 39657956492,148005508553,552364077718,2061450802319,7693439131560,28712305723921
%N A099488 Expansion of (1-x)^2/((1+x^2)(1-4x+x^2)).
%C A099488 A Chebyshev transform of the sequence A081294 which has with g.f. (1-2x)/(1-4x). The image of G(x) under the Chebyshev transform is (1/(1+x^2))G(x/(1+x^2)).
%H A099488 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,4,-1).
%F A099488 a(n)=4a(n-1)-2a(n-2)+4a(n-3); a(n)=sum{k=0..n, (0^k-2sin(pi*k/2))((2+sqrt(3))^(n-k+1)-(2-sqrt(3))^(n-k+1))/(2*sqrt(3))}; a(n)=sum{k=0..n, (0^k-2sin(pi*k/2))A001353(n-k)}; a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-1)^k*(4^(n-2k)+0^(n-2k))/2}.
%t A099488 CoefficientList[Series[(1-x)^2/((1+x^2)(1-4x+x^2)),{x,0,30}],x] (* or *) LinearRecurrence[{4,-2,4,-1},{1,2,7,28},30] (* _Harvey P. Dale_, Jun 23 2015 *)
%Y A099488 Cf. A099486, A099487.
%K A099488 easy,nonn
%O A099488 0,2
%A A099488 _Paul Barry_, Oct 18 2004