A112118 Unique sequence of numbers {1,2,3,...,9} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (9th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

1, 9, 9, 9, 6, 6, 3, 9, 6, 3, 9, 3, 3, 1, 7, 5, 9, 1, 8, 6, 2, 6, 4, 6, 7, 6, 4, 6, 3, 2, 5, 7, 2, 5, 7, 8, 1, 4, 9, 6, 3, 7, 6, 9, 1, 7, 7, 3, 7, 8, 7, 5, 7, 8, 9, 3, 8, 7, 9, 5, 3, 9, 9, 1, 5, 4, 5, 1, 7, 3, 1, 7, 8, 6, 1, 8, 4, 6, 8, 6, 5, 5, 9, 2, 6, 1, 5, 9, 8, 7, 2, 8, 8, 3, 2, 3, 9, 8, 2, 8, 4, 6, 1, 9, 4

Offset

1,2

Links

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

Example

G.f.: A(x) = x + 9*x^2 + 9*x^3 + 9*x^4 + 6*x^5 + 6*x^6 + 3*x^7 +...
then A(x) = B(B(B(B(B(B(B(B(B(x))))))))) where
B(x) = x + x^2 - 7*x^3 + 81*x^4 - 1122*x^5 + 16906*x^6 +...
is the g.f. of A112119.

Prog

(PARI) {a(n, m=9)=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. A112119, A112104-A112117, A112120-A112127.

Sequence in context: A146488 A051557 A146491 * A334450 A111590 A346584

Adjacent sequences: A112115 A112116 A112117 * A112119 A112120 A112121

Keyword

nonn

Author

Paul D. Hanna, Aug 27 2005

Status

approved