cp's OEIS Frontend

A112126 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.

%I A112126 #6 Mar 14 2015 00:05:31
%S A112126 1,13,13,13,13,13,13,13,13,13,13,13,13,13,12,12,12,12,12,12,12,12,12,
%T A112126 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 A112126 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 A112126 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 A112126 G.f.: A(x) = x + 13*x^2 + 13*x^3 + 13*x^4 + 13*x^5 + 13*x^6 +...
%e A112126 then A(x) = B(B(B(B(B(B(B(B(B(B(B(B(B(x))))))))))))) where
%e A112126 B(x) = x + x^2 - 11*x^3 + 193*x^4 - 4043*x^5 + 92233*x^6 +...
%e A112126 is the g.f. of A112127.
%o A112126 (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 A112126 Cf. A112127, A112104-A112125.
%K A112126 nonn
%O A112126 1,2
%A A112126 _Paul D. Hanna_, Aug 27 2005