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A112126
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Unique sequence of numbers {1,2,3,...,13} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (13-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, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 11, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 8, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 10, 3, 5, 13, 13, 13, 13, 13, 13, 13, 13, 12, 12, 3, 4, 4, 7, 7, 7, 7, 7, 7, 7, 6, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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EXAMPLE
| G.f.: A(x) = x + 13*x^2 + 13*x^3 + 13*x^4 + 13*x^5 + 13*x^6 +...
then A(x) = B(B(B(B(B(B(B(B(B(B(B(B(B(x))))))))))))) where
B(x) = x + x^2 - 11*x^3 + 193*x^4 - 4043*x^5 + 92233*x^6 +...
is the g.f. of A112127.
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PROG
| (PARI) {a(n, m=13)=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. A112127, A112104-A112125.
Sequence in context: A175850 A176306 A051392 * A010852 A201773 A072519
Adjacent sequences: A112123 A112124 A112125 * A112127 A112128 A112129
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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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