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A112116 Unique sequence of numbers {1,2,3,...,8} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (8th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0. 3
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; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..105.

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.

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)))}

CROSSREFS

Cf. A112117, A112104-A112115, A112118-A112127.

Sequence in context: A254615 A154841 A258984 * A228719 A021117 A305208

Adjacent sequences:  A112113 A112114 A112115 * A112117 A112118 A112119

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 27 2005

STATUS

approved

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)