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Search: id:A112122
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| A112122 |
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Unique sequence of numbers {1,2,3,...,11} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (11-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, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 10, 11, 11, 11, 11, 11, 11, 11, 11, 10, 2, 7, 1, 1, 1, 1, 1, 1, 1, 11, 1, 10, 1, 3, 3, 3, 3, 3, 3, 2, 2, 10, 11, 11, 3, 3, 3, 3, 3, 2, 6, 9, 5, 3, 2, 4, 4, 4, 4, 3, 5, 11, 6, 7
(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 + 11*x^2 + 11*x^3 + 11*x^4 + 11*x^5 +...
then A(x) = B(B(B(B(B(B(B(B(B(B(B(x))))))))))) where
B(x) = x + x^2 - 9*x^3 + 131*x^4 - 2279*x^5 + 43161*x^6 +...
is the g.f. of A112123.
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PROGRAM
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(PARI) {a(n, m=11)=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. A112123, A112104-A112121, A112124-A112127.
Sequence in context: A100755 A045538 A084066 this_sequence A010850 A113587 A083971
Adjacent sequences: A112119 A112120 A112121 this_sequence A112123 A112124 A112125
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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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