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%I #11 Oct 08 2018 18:34:17
%S 1,3,3,3,2,2,1,2,1,3,1,1,3,3,3,2,3,3,2,2,2,1,2,2,3,1,2,1,1,2,3,2,2,2,
%T 1,2,2,3,2,2,2,1,1,1,1,2,3,2,1,2,3,2,3,2,2,3,2,3,3,2,3,3,3,1,3,2,1,3,
%U 2,2,1,2,3,1,3,1,3,1,1,1,3,1,2,3,3,3,3,3,3,1,1,2,2,3,3,1,3,2,1,2,2,1,1,3,1
%N Unique sequence of numbers {1,2,3} where g.f. A(x) satisfies A(x) = B(B(B(x))) (3rd self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.
%e G.f.: A(x) = x + 3*x^2 + 3*x^3 + 3*x^4 + 2*x^5 + 2*x^6 + ...
%e then A(x) = B(B(B(x))) where
%e B(x) = x + x^2 - x^3 + 3*x^4 - 10*x^5 + 35*x^6 - 119*x^7 + ...
%e is the g.f. of A112107.
%o (PARI) {a(n,m=3)=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. A112107, A112104, A112105, A112108-A112127.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Aug 27 2005
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