A112116 Unique sequence of numbers {1,2,3,...,8} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (8th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

1, 8, 8, 4, 8, 4, 8, 8, 4, 8, 8, 4, 4, 8, 8, 4, 4, 8, 8, 2, 4, 6, 4, 6, 2, 4, 8, 8, 2, 2, 8, 4, 8, 2, 2, 8, 8, 6, 4, 4, 6, 2, 4, 3, 8, 5, 8, 8, 7, 5, 4, 3, 4, 6, 6, 2, 1, 7, 2, 7, 8, 8, 8, 2, 8, 8, 4, 2, 7, 8, 8, 5, 3, 4, 2, 6, 5, 1, 8, 7, 4, 1, 5, 4, 4, 7, 4, 2, 4, 7, 6, 4, 6, 2, 6, 3, 5, 6, 7, 2, 5, 7, 8, 8, 7

Offset: 1

Author

Paul D. Hanna, Aug 27 2005

Keywords

• nonn

Examples

			G.f.: A(x) = x + 8*x^2 + 8*x^3 + 4*x^4 + 8*x^5 + 4*x^6 + 8*x^7 +...
then A(x) = B(B(B(B(B(B(B(B(x)))))))) where
B(x) = x + x^2 - 6*x^3 + 60*x^4 - 720*x^5 + 9398*x^6 - 126958*x^7 +...
is the g.f. of A112117.
		

Crossrefs

Cf. A112117, A112104-A112115, A112118-A112127.

Programs

PARI

{a(n,m=8)=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)))}