A112122 Unique sequence of numbers {1,2,3,...,11} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (11th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 10, 11, 11, 11, 11, 11, 11, 11, 11, 10, 2, 7, 1, 1, 1, 1, 1, 1, 1, 11, 1, 10, 1, 3, 3, 3, 3, 3, 3, 2, 2, 10, 11, 11, 3, 3, 3, 3, 3, 2, 6, 9, 5, 3, 2, 4, 4, 4, 4, 3, 5, 11, 6, 7

Offset

1,2

Links

Table of n, a(n) for n=1..87.

Example

G.f.: A(x) = x + 11*x^2 + 11*x^3 + 11*x^4 + 11*x^5 +...
then A(x) = B(B(B(B(B(B(B(B(B(B(B(x))))))))))) where
B(x) = x + x^2 - 9*x^3 + 131*x^4 - 2279*x^5 + 43161*x^6 +...
is the g.f. of A112123.

Prog

(PARI) {a(n, m=11)=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. A112123, A112104-A112121, A112124-A112127.

Sequence in context: A084066 A231472 A319150 * A290856 A010850 A317244

Adjacent sequences: A112119 A112120 A112121 * A112123 A112124 A112125

Keyword

nonn

Author

Paul D. Hanna, Aug 27 2005

Status

approved