A112110 - OEIS

%I #10 Oct 08 2018 18:35:45

%S 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,

%T 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,

%U 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

%N 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.

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

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

%e B(x) = x + x^2 - 3*x^3 + 17*x^4 - 115*x^5 + 841*x^6 + ...

%e is the g.f. of A112111.

%o (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)))}

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

%K nonn

%O 1,2

%A _Paul D. Hanna_, Aug 27 2005