A087222 G.f. satisfies A(x) = 1 + x*A(x)*f(x)^3, where f(x) = Sum_{k>=0} x^((4^k-1)/3).

1, 1, 4, 10, 26, 69, 184, 488, 1294, 3436, 9116, 24190, 64190, 170334, 451994, 1199400, 3182706, 8445556, 22410946, 59469200, 157806184, 418751069, 1111188772, 2948626472, 7824411358, 20762688580, 55095420880, 146200015984

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Formula

a(n) = A087221(3n).

Example

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*A(x)*(1 + 3x + 3x^2 + x^3 + 3x^5 + 6x^6 + ...)
= 1 + x + 4x^2 + 10x^3 + 26x^4 + 69x^5 + 184x^6 + ...

Mathematica

nmax = 30; CoefficientList[Series[1/(1 - Sum[x^((4^k - 1)/3), {k, 0, nmax}]^3*x), {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 11 2020 *)

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))

Crossrefs

Cf. A087221, A087232, A087224.

Sequence in context: A200663 A200464 A099234 * A130583 A240048 A105999

Adjacent sequences: A087219 A087220 A087221 * A087223 A087224 A087225

Keyword

nonn

Author

Paul D. Hanna, Aug 27 2003

Status

approved