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Search: id:A112109
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| A112109 |
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G.f. A(x) satisfies A(A(A(A(x)))) = B(x) (4-th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,4}, with B(0) = 0. |
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+0
4
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| 1, 1, -2, 8, -38, 194, -992, 4777, -19831, 56116, 48008, -2062286, 16053636, -70193968, 155216743, -968038798, 23817048561, -233579083166, 333773365, 21684104628935, -121906541882294, -2171063003748135, 30425707365005935, 192144123118329872
(list; graph; listen)
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OFFSET
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1,3
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EXAMPLE
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A(x) = x + x^2 - 2*x^3 + 8*x^4 - 38*x^5 + 194*x^6 - 992*x^7 +...
where A(A(A(A(x)))) =
x + 4*x^2 + 4*x^3 + 2*x^4 + 4*x^5 + 2*x^6 + 4*x^7 + 4*x^8 +...
is the g.f. of A112108.
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PROGRAM
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(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); return(polcoeff(F, n, x)))}
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CROSSREFS
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Cf. A112108, A112104-A112107, A112110-A112127.
Sequence in context: A123164 A002003 A059423 this_sequence A026939 A047098 A108246
Adjacent sequences: A112106 A112107 A112108 this_sequence A112110 A112111 A112112
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KEYWORD
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sign
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 27 2005
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