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 A087218 #10 Nov 19 2017 01:47:34
%S A087218 1,1,3,6,13,30,66,147,327,726,1614,3588,7974,17725,39399,87573,194655,
%T A087218 432669,961716,2137659,4751490,10561392,23475378,52179987,115983270,
%U A087218 257802273,573031011,1273706934,2831137095,6292921101,13987615113
%N A087218 Satisfies A(x) = 1 + x*A(x)*f(x)^2, where f(x) = Sum_{k>=0} x^((3^n-1)/2) and f(x)^2 = 2 - f(x^2) + 2*Sum_{n>0} x^A023745(n).
%F A087218 a(n) = A078932(2n). a(m) = 1 (mod 3) when m = (3^n - 1)/2, otherwise a(m) = 0 (mod 3).
%e A087218 Given f(x) = 1 + x + x^4 + x^13 + x^40 + x^121 + ... so that f(x)^2 = 1 + 2x + x^2 + 2x^4 + 2x^5 + x^8 + 2*x^13 + ... then A(x) = 1 + x*A(x)*(1 + 2x + x^2 + 2x^4 + 2x^5 + x^8 + ...) = 1 + x + 3x^2 + 6x^3 + 13x^4 + 30x^5 + ...
%o A087218 (PARI) a(n)=local(A,m); if(n<1,1,m=1; A=1+O(x); while(m<=2*n,m*=3; A=1/(1/subst(A,x,x^3)-x)); polcoeff(A,2*n));
%Y A087218 Cf. A078932, A023745, A087219.
%K A087218 nonn
%O A087218 0,3
%A A087218 _Paul D. Hanna_, Aug 26 2003