A087218 Satisfies A(x) = 1 + 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).

1, 1, 3, 6, 13, 30, 66, 147, 327, 726, 1614, 3588, 7974, 17725, 39399, 87573, 194655, 432669, 961716, 2137659, 4751490, 10561392, 23475378, 52179987, 115983270, 257802273, 573031011, 1273706934, 2831137095, 6292921101, 13987615113

Offset

0,3

Links

Table of n, a(n) for n=0..30.

Formula

a(n) = A078932(2n). a(m) = 1 (mod 3) when m = (3^n - 1)/2, otherwise a(m) = 0 (mod 3).

Example

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*A(x)*(1 + 2x + x^2 + 2x^4 + 2x^5 + x^8 + ...) = 1 + x + 3x^2 + 6x^3 + 13x^4 + 30x^5 + ...

Prog

(PARI) a(n)=local(A, m); if(n<1, 1, m=1; A=1+O(x); while(m<=2*n, m*=3; A=1/(1/subst(A, x, x^3)-x)); polcoeff(A, 2*n));

Crossrefs

Cf. A078932, A023745, A087219.

Sequence in context: A213674 A108639 A327795 * A098075 A137584 A201631

Adjacent sequences: A087215 A087216 A087217 * A087219 A087220 A087221

Keyword

nonn

Author

Paul D. Hanna, Aug 26 2003

Status

approved