%I #6 Oct 01 2023 20:13:07
%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 9th cyclotomic polynomial. The g.f. is a Chebyshev transform of that of (1)^n*A052931(n) by the Chebyshev mapping g(x)>(1/(1+x^2))g(x/(1+x^2)). The reciprocal of the 9th cyclotomic polynomial A014018 is given by sum{k=0..n, A099917(nk)(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(nk, k)(1)^k*sum{j=0..n2k, C(j, n2k2j)3^k(1/3)^(n2k)}}; a(n)=sum{k=0..n, A014018(nk)C(2, k/2)(1+(1)^k)/2}.
%Y Cf. A099916.
%K easy,sign
%O 0,3
%A _Paul Barry_, Oct 30 2004
