A112109 G.f. A(x) satisfies A(A(A(A(x)))) = B(x) (4th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,4}, with B(0) = 0.

1, 1, -2, 8, -38, 194, -992, 4777, -19831, 56116, 48008, -2062286, 16053636, -70193968, 155216743, -968038798, 23817048561, -233579083166, 333773365, 21684104628935, -121906541882294, -2171063003748135, 30425707365005935, 192144123118329872

Offset

1,3

Links

Table of n, a(n) for n=1..24.

Example

A(x) = x + x^2 - 2*x^3 + 8*x^4 - 38*x^5 + 194*x^6 - 992*x^7 +...
where A(A(A(A(x)))) =
x + 4*x^2 + 4*x^3 + 2*x^4 + 4*x^5 + 2*x^6 + 4*x^7 + 4*x^8 +...
is the g.f. of A112108.

Prog

(PARI) {a(n, m=4)=local(F=x+x^2+x*O(x^n), G); if(n<1, 0, for(k=3, n, G=F+x*O(x^k); for(i=1, m-1, G=subst(F, x, G)); F=F-((polcoeff(G, k)-1)\m)*x^k); return(polcoeff(F, n, x)))}

Crossrefs

Cf. A112108, A112104-A112107, A112110-A112127.

Sequence in context: A123164 A264229 A059423 * A345178 A026939 A291088

Adjacent sequences: A112106 A112107 A112108 * A112110 A112111 A112112

Keyword

sign

Author

Paul D. Hanna, Aug 27 2005

Status

approved