A112112 - OEIS

%I #11 Oct 08 2018 18:35:26

%S 1,6,6,3,4,4,6,2,5,3,3,5,3,2,5,3,3,4,5,4,3,2,6,4,3,6,2,5,6,4,2,5,4,5,

%T 1,1,1,4,4,2,3,6,6,5,5,4,3,5,5,2,2,1,3,6,1,5,2,6,5,4,3,4,6,6,5,5,6,1,

%U 5,6,6,3,3,1,5,4,5,1,5,2,2,4,3,4,2,1,6,1,3,2,4,1,3,5,3,1,3,2,6,2,5,1,3,6,2

%N Unique sequence of numbers {1,2,3,...,6} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (6th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

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

%e then A(x) = B(B(B(B(B(B(x)))))) where B(x) = x + x^2 - 4*x^3 + 28*x^4 - 236*x^5 + 2159*x^6 + ... is the g.f. of A112113.

%o (PARI) {a(n,m=6)=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. A112113, A112104-A112111, A112114-A112127.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Aug 27 2005