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A112110
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Unique sequence of numbers {1,2,3,4,5} where g.f. A(x) satisfies A(x) = B(B(B(B(B(x))))) (5-th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.
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3
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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
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..105.
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EXAMPLE
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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.
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PROG
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(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)))}
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CROSSREFS
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Cf. A112111, A112104-A112109, A112112-A112127.
Sequence in context: A083945 A125563 A093704 * A142864 A098598 A010716
Adjacent sequences: A112107 A112108 A112109 * A112111 A112112 A112113
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Aug 27 2005
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STATUS
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approved
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