|
%I #12 Oct 11 2020 05:52:15
%S 1,3,7,19,50,133,352,935,2482,6584,17473,46365,123034,326478,866338,
%T 2298895,6100296,16187616,42955106,113984740,302467434,802621041,
%U 2129817812,5651638433,14997065388,39795888008,105601506802
%N 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).
%F a(n) = A087221(3n+2).
%e Given f(x) = 1 + x + x^5 + x^21 + x^85 + x^341 + ...
%e so that f(x)^2 = 1 + 2x + x^2 + 2x^5 + 2x^6 + x^10 + 2x^21 + ...
%e and f(x)^3 = 1 + 3x + 3x^2 + x^3 + 3x^5 + 6x^6 + 3x^7 + 3x^10 + ...
%e then A(x) = (1 + 2x + x^2 + 2x^5 + ...) + x*A(x)*(1 + 3x + 3x^2 + x^3 + 3x^5 + ...)
%e = 1 + 3x + 7x^2 + 19x^3 + 50x^4 + 133x^5 + 352x^6 + ...
%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+2))
%Y Cf. A087221, A087222, A087223.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Aug 27 2003
|
