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Search: id:A112126
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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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4
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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; listen)
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OFFSET
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1,2
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EXAMPLE
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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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PROGRAM
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(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
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Cf. A112127, A112104-A112125.
Sequence in context: A004454 A113548 A051392 this_sequence A010852 A072519 A060362
Adjacent sequences: A112123 A112124 A112125 this_sequence A112127 A112128 A112129
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 27 2005
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