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Search: id:A112106
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| A112106 |
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Unique sequence of numbers {1,2,3} where g.f. A(x) satisfies A(x) = B(B(B(x))) (3-rd self-COMPOSE) such that B(x) is an integer series, with A(0) = 0. |
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+0
4
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| 1, 3, 3, 3, 2, 2, 1, 2, 1, 3, 1, 1, 3, 3, 3, 2, 3, 3, 2, 2, 2, 1, 2, 2, 3, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 1, 1, 1, 1, 2, 3, 2, 1, 2, 3, 2, 3, 2, 2, 3, 2, 3, 3, 2, 3, 3, 3, 1, 3, 2, 1, 3, 2, 2, 1, 2, 3, 1, 3, 1, 3, 1, 1, 1, 3, 1, 2, 3, 3, 3, 3, 3, 3, 1, 1, 2, 2, 3, 3, 1, 3, 2, 1, 2, 2, 1, 1, 3, 1
(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 + 3*x^2 + 3*x^3 + 3*x^4 + 2*x^5 + 2*x^6 +...
then A(x) = B(B(B(x))) where
B(x) = x + x^2 - x^3 + 3*x^4 - 10*x^5 + 35*x^6 - 119*x^7 +...
is the g.f. of A112107.
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PROGRAM
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(PARI) {a(n, m=3)=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. A112107, A112104, A112105, A112108-A112127.
Sequence in context: A016651 A135877 A136218 this_sequence A010608 A086139 A074804
Adjacent sequences: A112103 A112104 A112105 this_sequence A112107 A112108 A112109
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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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