A112110 Unique sequence of numbers {1,2,3,4,5} where g.f. A(x) satisfies A(x) = B(B(B(B(B(x))))) (5th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

1, 5, 5, 5, 5, 5, 4, 4, 4, 4, 3, 1, 1, 1, 5, 3, 1, 1, 5, 3, 4, 3, 2, 1, 5, 4, 1, 4, 1, 5, 1, 4, 5, 4, 2, 1, 5, 2, 5, 4, 5, 5, 4, 1, 1, 5, 4, 3, 5, 1, 5, 2, 2, 3, 1, 3, 2, 5, 2, 5, 3, 2, 3, 5, 2, 1, 2, 3, 1, 5, 1, 4, 5, 4, 3, 3, 2, 4, 2, 3, 4, 5, 2, 5, 5, 2, 4, 2, 3, 5, 3, 2, 4, 2, 2, 1, 1, 2, 3, 4, 5, 3, 3, 1, 5

Offset: 1

Author

Paul D. Hanna, Aug 27 2005

Keywords

• nonn

Examples

			G.f.: A(x) = x + 5*x^2 + 5*x^3 + 5*x^4 + 5*x^5 + 5*x^6 + ...
then A(x) = B(B(B(B(B(x))))) where
B(x) = x + x^2 - 3*x^3 + 17*x^4 - 115*x^5 + 841*x^6 + ...
is the g.f. of A112111.
		

Crossrefs

Cf. A112111, A112104-A112109, A112112-A112127.

Programs

PARI

{a(n,m=5)=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)))}