A112126 Unique sequence of numbers {1,2,3,...,13} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (13th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

1, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 11, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 8, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 10, 3, 5, 13, 13, 13, 13, 13, 13, 13, 13, 12, 12, 3, 4, 4, 7, 7, 7, 7, 7, 7, 7, 6, 3

Offset

1,2

Links

Table of n, a(n) for n=1..88.

Example

G.f.: A(x) = x + 13*x^2 + 13*x^3 + 13*x^4 + 13*x^5 + 13*x^6 +...
then A(x) = B(B(B(B(B(B(B(B(B(B(B(B(B(x))))))))))))) where
B(x) = x + x^2 - 11*x^3 + 193*x^4 - 4043*x^5 + 92233*x^6 +...
is the g.f. of A112127.

Prog

(PARI) {a(n, m=13)=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. A112127, A112104-A112125.

Sequence in context: A051392 A291431 A291474 * A010852 A290686 A291569

Adjacent sequences: A112123 A112124 A112125 * A112127 A112128 A112129

Keyword

nonn

Author

Paul D. Hanna, Aug 27 2005

Status

approved