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%I #14 Oct 11 2020 05:52:09
%S 1,1,4,10,26,69,184,488,1294,3436,9116,24190,64190,170334,451994,
%T 1199400,3182706,8445556,22410946,59469200,157806184,418751069,
%U 1111188772,2948626472,7824411358,20762688580,55095420880,146200015984
%N G.f. satisfies A(x) = 1 + x*A(x)*f(x)^3, where f(x) = Sum_{k>=0} x^((4^k-1)/3).
%F a(n) = A087221(3n).
%e Given f(x) = 1 + x + x^5 + x^21 + x^85 + x^341 + ...
%e so that f(x)^3 = 1 + 3x + 3x^2 + x^3 + 3x^5 + 6x^6 + 3x^7 + 3x^10 + ...
%e then A(x) = 1 + x*A(x)*(1 + 3x + 3x^2 + x^3 + 3x^5 + 6x^6 + ...)
%e = 1 + x + 4x^2 + 10x^3 + 26x^4 + 69x^5 + 184x^6 + ...
%t nmax = 30; CoefficientList[Series[1/(1 - Sum[x^((4^k - 1)/3), {k, 0, nmax}]^3*x), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 11 2020 *)
%o (PARI) a(n)=local(A,m); if(n<1,n==0,m=1; A=1+O(x); while(m<=3*n+3,m*=4; A=1/(1/subst(A,x,x^4)-x)); polcoeff(A,3*n))
%Y Cf. A087221, A087232, A087224.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 27 2003
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