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A112108
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Unique sequence of numbers {1,2,3,4} where g.f. A(x) satisfies A(x) = B(B(B(B(x)))) (4-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, 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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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EXAMPLE
| G.f.: A(x) = x + 4*x^2 + 4*x^3 + 2*x^4 + 4*x^5 + 2*x^6 +...
then A(x) = B(B(B(B(x)))) where
B(x) = x + x^2 - 2*x^3 + 8*x^4 - 38*x^5 + 194*x^6 - 992*x^7 +...
is the g.f. of A112109.
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PROG
| (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)))}
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CROSSREFS
| Cf. A112109, A112104-A112107, A112110-A112127.
Sequence in context: A068923 A103714 A193514 * A021230 A011321 A064860
Adjacent sequences: A112105 A112106 A112107 * A112109 A112110 A112111
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 27 2005
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