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A112116
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Unique sequence of numbers {1,2,3,...,8} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (8-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, 8, 8, 4, 8, 4, 8, 8, 4, 8, 8, 4, 4, 8, 8, 4, 4, 8, 8, 2, 4, 6, 4, 6, 2, 4, 8, 8, 2, 2, 8, 4, 8, 2, 2, 8, 8, 6, 4, 4, 6, 2, 4, 3, 8, 5, 8, 8, 7, 5, 4, 3, 4, 6, 6, 2, 1, 7, 2, 7, 8, 8, 8, 2, 8, 8, 4, 2, 7, 8, 8, 5, 3, 4, 2, 6, 5, 1, 8, 7, 4, 1, 5, 4, 4, 7, 4, 2, 4, 7, 6, 4, 6, 2, 6, 3, 5, 6, 7, 2, 5, 7, 8, 8, 7
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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EXAMPLE
| G.f.: A(x) = x + 8*x^2 + 8*x^3 + 4*x^4 + 8*x^5 + 4*x^6 + 8*x^7 +...
then A(x) = B(B(B(B(B(B(B(B(x)))))))) where
B(x) = x + x^2 - 6*x^3 + 60*x^4 - 720*x^5 + 9398*x^6 - 126958*x^7 +...
is the g.f. of A112117.
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PROG
| (PARI) {a(n, m=8)=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. A112117, A112104-A112115, A112118-A112127.
Sequence in context: A154845 A126600 A154841 * A021117 A081799 A154186
Adjacent sequences: A112113 A112114 A112115 * A112117 A112118 A112119
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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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