A112116 - OEIS

%I #6 Mar 12 2015 19:56:05

%S 1,8,8,4,8,4,8,8,4,8,8,4,4,8,8,4,4,8,8,2,4,6,4,6,2,4,8,8,2,2,8,4,8,2,

%T 2,8,8,6,4,4,6,2,4,3,8,5,8,8,7,5,4,3,4,6,6,2,1,7,2,7,8,8,8,2,8,8,4,2,

%U 7,8,8,5,3,4,2,6,5,1,8,7,4,1,5,4,4,7,4,2,4,7,6,4,6,2,6,3,5,6,7,2,5,7,8,8,7

%N Unique sequence of numbers {1,2,3,...,8} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (8th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

%e G.f.: A(x) = x + 8*x^2 + 8*x^3 + 4*x^4 + 8*x^5 + 4*x^6 + 8*x^7 +...

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

%e B(x) = x + x^2 - 6*x^3 + 60*x^4 - 720*x^5 + 9398*x^6 - 126958*x^7 +...

%e is the g.f. of A112117.

%o (PARI) {a(n,m=8)=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. A112117, A112104-A112115, A112118-A112127.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Aug 27 2005