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%I #7 Jun 13 2015 00:51:34
%S 1,0,2,1,1,2,0,1,0,-1,0,-2,-1,-1,-2,0,-1,0,1,0,2,1,1,2,0,1,0,-1,0,-2,
%T -1,-1,-2,0,-1,0,1,0,2,1,1,2,0,1,0,-1,0,-2,-1,-1,-2,0,-1,0,1,0,2,1,1,
%U 2,0,1,0,-1,0,-2,-1,-1,-2,0,-1,0,1,0,2,1,1,2,0,1,0,-1,0,-2,-1,-1,-2,0,-1,0,1,0,2,1,1,2,0,1,0,-1,0
%N Expansion of (1+x^2)^2/(1-x^3+x^6).
%C The denominator is the 18th cyclotomic polynomial. The g.f. is a Chebyshev transform of that of A052931, by the Chebyshev mapping g(x)->(1/(1+x^2))g(x/(1+x^2)). The reciprocal of the 18th cyclotomic polynomial A014027 is given by sum{k=0..n, A099916(n-k)(k/2+1)(-1)^(k/2)(1+(-1)^k)/2}.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,0,0,-1)
%F a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*sum{j=0..n-2k, C(j, n-2k-2j)3^(3j-n+2k)}}; a(n)=sum{k=0..n, A014027(n-k)C(2, k/2)(1+(-1)^k)/2}.
%K easy,sign
%O 0,3
%A _Paul Barry_, Oct 30 2004
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