A112120 Unique sequence of numbers {1,2,3,...,10} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (10th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

1, 10, 10, 5, 10, 5, 8, 3, 4, 3, 2, 1, 9, 2, 8, 1, 7, 4, 9, 4, 7, 8, 2, 4, 5, 5, 6, 5, 6, 6, 6, 5, 6, 7, 3, 1, 2, 10, 10, 10, 5, 7, 10, 1, 4, 7, 1, 1, 5, 7, 2, 8, 9, 4, 3, 7, 5, 10, 4, 4, 9, 8, 7, 8, 4, 6, 7, 1, 2, 2, 3, 5, 9, 1, 10, 2, 5, 4, 5, 9, 3, 4, 10, 1, 1, 10, 4, 2, 6, 4, 8, 2, 2, 4, 9, 2, 10, 8, 4, 7

Offset

1,2

Links

Table of n, a(n) for n=1..100.

Example

G.f.: A(x) = x + 10*x^2 + 10*x^3 + 5*x^4 + 10*x^5 + 5*x^6 +...
then A(x) = B(B(B(B(B(B(B(B(B(B(x)))))))))) where
B(x) = x + x^2 - 8*x^3 + 104*x^4 - 1619*x^5 + 27437*x^6 +...
is the g.f. of A112121.

Prog

(PARI) {a(n, m=10)=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. A112121, A112104-A112119, A112122-A112127.

Sequence in context: A275626 A071531 A276467 * A099401 A263450 A087028

Adjacent sequences: A112117 A112118 A112119 * A112121 A112122 A112123

Keyword

nonn

Author

Paul D. Hanna, Aug 27 2005

Status

approved