A112108 Unique sequence of numbers {1,2,3,4} where g.f. A(x) satisfies A(x) = B(B(B(B(x)))) (4th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

1, 4, 4, 2, 4, 2, 4, 4, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 3, 4, 3, 2, 4, 1, 2, 4, 2, 3, 1, 4, 2, 4, 3, 1, 4, 4, 4, 2, 2, 2, 3, 3, 2, 3, 2, 2, 4, 1, 4, 2, 2, 1, 4, 3, 3, 3, 1, 1, 3, 3, 4, 4, 3, 3, 3, 3, 1, 4, 4, 3, 2, 4, 2, 2, 2, 1, 3, 4, 2, 3, 3, 1, 4, 2, 3, 1, 1, 3, 3, 4, 2, 4, 3, 1, 4, 3, 2, 1, 1, 1, 2, 1, 4, 4

Offset: 1

Author

Paul D. Hanna, Aug 27 2005

Keywords

• nonn

Examples

			G.f.: A(x) = x + 4*x^2 + 4*x^3 + 2*x^4 + 4*x^5 + 2*x^6 + ...
then A(x) = B(B(B(B(x)))) where
B(x) = x + x^2 - 2*x^3 + 8*x^4 - 38*x^5 + 194*x^6 - 992*x^7 + ...
is the g.f. of A112109.
		

Crossrefs

Cf. A112109, A112104-A112107, A112110-A112127.

Programs

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); G=F+x*O(x^n);for(i=1,m-1,G=subst(F,x,G)); return(polcoeff(G,n,x)))}