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A112110
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.
3
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, 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, 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
OFFSET
1,2
EXAMPLE
G.f.: A(x) = x + 5*x^2 + 5*x^3 + 5*x^4 + 5*x^5 + 5*x^6 + ...
then A(x) = B(B(B(B(B(x))))) where
B(x) = x + x^2 - 3*x^3 + 17*x^4 - 115*x^5 + 841*x^6 + ...
is the g.f. of A112111.
PROG
(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)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 27 2005
STATUS
approved