cp's OEIS Frontend

A087219 Satisfies A(x) = f(x) + 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). Also, A(x) = f(x)*B(x), where B(x) = Sum_{k>=0} A087218(k)*x^k.

%I A087219 #10 Nov 19 2017 01:38:53
%S A087219 1,2,4,9,20,44,99,219,487,1083,2406,5349,11889,26426,58739,130563,
%T A087219 290208,645062,1433814,3187014,7083951,15745878,34999212,77794638,
%U A087219 172918335,384354909,854326387,1898957331,4220914872,9382055124
%N A087219 Satisfies A(x) = f(x) + 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). Also, A(x) = f(x)*B(x), where B(x) = Sum_{k>=0} A087218(k)*x^k.
%F A087219 a(n) = A078932(2n+1). a(m) = 1 (mod 3) when m = (3^n-1)/2 (mod 3), else a(m) = 2 (mod 3) when m = A023745(n), otherwise a(m) = 0 (mod 3).
%e A087219 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 + x^4 + ...) + x*A(x)*(1 + 2x + x^2 + 2x^4 + 2x^5 + ...) = 1 + 2x + 4x^2 + 9x^3 + 20x^4 + 44x^5 + ...
%o A087219 (PARI) a(n)=local(A,m); if(n<1,1,m=1; A=1+O(x); while(m<=2*n+1,m*=3; A=1/(1/subst(A,x,x^3)-x)); polcoeff(A,2*n+1));
%Y A087219 Cf. A078932, A087218.
%K A087219 nonn
%O A087219 0,2
%A A087219 _Paul D. Hanna_, Aug 27 2003