A112124 Unique sequence of numbers {1,2,3,...,12} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (12th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

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

Offset

1,2

Links

Table of n, a(n) for n=1..91.

Example

G.f.: A(x) = x + 12*x^2 + 12*x^3 + 6*x^4 + 8*x^5 + 8*x^6 +...
then A(x) = B(B(B(B(B(B(B(B(B(B(B(B(x)))))))))))) where
B(x) = x + x^2 - 10*x^3 + 160*x^4 - 3061*x^5 + 63775*x^6 +...
is the g.f. of A112125.

Prog

(PARI) {a(n, m=12)=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. A112125, A112104-A112123, A112126, A112127.

Sequence in context: A097824 A133208 A118877 * A268916 A362236 A069873

Adjacent sequences: A112121 A112122 A112123 * A112125 A112126 A112127

Keyword

nonn

Author

Paul D. Hanna, Aug 27 2005

Status

approved