A112126 - OEIS

%I #6 Mar 14 2015 00:05:31

%S 1,13,13,13,13,13,13,13,13,13,13,13,13,13,12,12,12,12,12,12,12,12,12,

%T 12,12,12,11,9,9,9,9,9,9,9,9,9,9,9,8,1,3,3,3,3,3,3,3,3,3,3,2,8,9,6,6,

%U 6,6,6,6,6,6,6,5,10,3,5,13,13,13,13,13,13,13,13,12,12,3,4,4,7,7,7,7,7,7,7,6,3

%N Unique sequence of numbers {1,2,3,...,13} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (13th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

%e G.f.: A(x) = x + 13*x^2 + 13*x^3 + 13*x^4 + 13*x^5 + 13*x^6 +...

%e then A(x) = B(B(B(B(B(B(B(B(B(B(B(B(B(x))))))))))))) where

%e B(x) = x + x^2 - 11*x^3 + 193*x^4 - 4043*x^5 + 92233*x^6 +...

%e is the g.f. of A112127.

%o (PARI) {a(n,m=13)=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)))}

%Y Cf. A112127, A112104-A112125.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Aug 27 2005