A087224 - OEIS

A087224

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).

1, 3, 7, 19, 50, 133, 352, 935, 2482, 6584, 17473, 46365, 123034, 326478, 866338, 2298895, 6100296, 16187616, 42955106, 113984740, 302467434, 802621041, 2129817812, 5651638433, 14997065388, 39795888008, 105601506802

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

FORMULA

a(n) = A087221(3n+2).

EXAMPLE

Given f(x) = 1 + x + x^5 + x^21 + x^85 + x^341 + ...

so that f(x)^2 = 1 + 2x + x^2 + 2x^5 + 2x^6 + x^10 + 2x^21 + ...

and f(x)^3 = 1 + 3x + 3x^2 + x^3 + 3x^5 + 6x^6 + 3x^7 + 3x^10 + ...

then A(x) = (1 + 2x + x^2 + 2x^5 + ...) + x*A(x)*(1 + 3x + 3x^2 + x^3 + 3x^5 + ...)

= 1 + 3x + 7x^2 + 19x^3 + 50x^4 + 133x^5 + 352x^6 + ...

PROG

(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))

CROSSREFS

Cf. A087221, A087222, A087223.

Sequence in context: A147234 A171854 A182895 * A308398 A341703 A078059

Adjacent sequences: A087221 A087222 A087223 * A087225 A087226 A087227

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 27 2003

STATUS

approved