A112124 Unique sequence of numbers {1,2,3,...,12} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (12th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

1, 12, 12, 6, 8, 8, 12, 2, 8, 2, 10, 9, 10, 10, 4, 5, 4, 7, 10, 10, 12, 7, 12, 8, 8, 9, 10, 7, 11, 12, 2, 9, 12, 10, 11, 7, 6, 5, 4, 5, 10, 7, 9, 1, 9, 5, 12, 12, 2, 10, 6, 9, 9, 6, 2, 1, 9, 3, 7, 10, 4, 11, 10, 3, 6, 10, 6, 10, 12, 11, 8, 1, 2, 4, 7, 2, 8, 6, 9, 12, 8, 2, 3, 2, 4, 3, 6, 12, 6, 11, 4

Offset: 1

Author

Paul D. Hanna, Aug 27 2005

Keywords

• nonn

Examples

			G.f.: A(x) = x + 12*x^2 + 12*x^3 + 6*x^4 + 8*x^5 + 8*x^6 +...
then A(x) = B(B(B(B(B(B(B(B(B(B(B(B(x)))))))))))) where
B(x) = x + x^2 - 10*x^3 + 160*x^4 - 3061*x^5 + 63775*x^6 +...
is the g.f. of A112125.
		

Crossrefs

Cf. A112125, A112104-A112123, A112126, A112127.

Programs

PARI

{a(n,m=12)=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)))}