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%I A112108 #10 Oct 08 2018 18:36:03
%S A112108 1,4,4,2,4,2,4,4,2,4,4,2,2,4,4,2,2,4,4,3,4,3,2,4,1,2,4,2,3,1,4,2,4,3,
%T A112108 1,4,4,4,2,2,2,3,3,2,3,2,2,4,1,4,2,2,1,4,3,3,3,1,1,3,3,4,4,3,3,3,3,1,
%U A112108 4,4,3,2,4,2,2,2,1,3,4,2,3,3,1,4,2,3,1,1,3,3,4,2,4,3,1,4,3,2,1,1,1,2,1,4,4
%N A112108 Unique sequence of numbers {1,2,3,4} where g.f. A(x) satisfies A(x) = B(B(B(B(x)))) (4th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.
%e A112108 G.f.: A(x) = x + 4*x^2 + 4*x^3 + 2*x^4 + 4*x^5 + 2*x^6 + ...
%e A112108 then A(x) = B(B(B(B(x)))) where
%e A112108 B(x) = x + x^2 - 2*x^3 + 8*x^4 - 38*x^5 + 194*x^6 - 992*x^7 + ...
%e A112108 is the g.f. of A112109.
%o A112108 (PARI) {a(n,m=4)=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 A112108 Cf. A112109, A112104-A112107, A112110-A112127.
%K A112108 nonn
%O A112108 1,2
%A A112108 _Paul D. Hanna_, Aug 27 2005

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