A087224 G.f. satisfies A(x) = f(x)^2 + x*A(x)*f(x)^3, where f(x) = Sum_{k>=0} x^((4^k-1)/3).
1, 3, 7, 19, 50, 133, 352, 935, 2482, 6584, 17473, 46365, 123034, 326478, 866338, 2298895, 6100296, 16187616, 42955106, 113984740, 302467434, 802621041, 2129817812, 5651638433, 14997065388, 39795888008, 105601506802
Offset: 0
Keywords
Examples
Given f(x) = 1 + x + x^5 + x^21 + x^85 + x^341 + ... so that f(x)^2 = 1 + 2x + x^2 + 2x^5 + 2x^6 + x^10 + 2x^21 + ... and f(x)^3 = 1 + 3x + 3x^2 + x^3 + 3x^5 + 6x^6 + 3x^7 + 3x^10 + ... then A(x) = (1 + 2x + x^2 + 2x^5 + ...) + x*A(x)*(1 + 3x + 3x^2 + x^3 + 3x^5 + ...) = 1 + 3x + 7x^2 + 19x^3 + 50x^4 + 133x^5 + 352x^6 + ...
Programs
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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+2))
Formula
a(n) = A087221(3n+2).