A087223 G.f. satisfies A(x) = f(x) + x*A(x)*f(x)^3, where f(x) = Sum_{k>=0} x^((4^k-1)/3).

1, 2, 5, 14, 36, 96, 254, 676, 1792, 4756, 12621, 33490, 88868, 235818, 625764, 1660510, 4406296, 11692452, 31026836, 82332140, 218474784, 579739960, 1538385398, 4082226194, 10832507040, 28744906148, 76276860598, 202406625820

Offset: 0

Author

Paul D. Hanna, Aug 27 2003

Keywords

• nonn

Examples

			Given f(x) = 1 + x + x^5 + x^21 + x^85 + x^341 + ...
so that f(x)^3 = 1 + 3x + 3x^2 + x^3 + 3x^5 + 6x^6 + 3x^7 + 3x^10 + ...
then A(x) = (1 + x + x^5 + ...) + x*A(x)*(1 + 3x + 3x^2 + x^3 + 3x^5 + 6x^6 + ...)
= 1 + 2x + 5x^2 + 14x^3 + 36x^4 + 96x^5 + 254x^6 + ...
		

Crossrefs

Cf. A087221, A087222, A087224.

Programs

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+1))

Formula

a(n) = A087221(3n+1).