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.

1, 2, 4, 9, 20, 44, 99, 219, 487, 1083, 2406, 5349, 11889, 26426, 58739, 130563, 290208, 645062, 1433814, 3187014, 7083951, 15745878, 34999212, 77794638, 172918335, 384354909, 854326387, 1898957331, 4220914872, 9382055124

Offset: 0

Author

Paul D. Hanna, Aug 27 2003

Keywords

• nonn

Examples

			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 + ...
		

Crossrefs

Cf. A078932, A087218.

Programs

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));

Formula

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).