A112112 Unique sequence of numbers {1,2,3,...,6} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (6th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

1, 6, 6, 3, 4, 4, 6, 2, 5, 3, 3, 5, 3, 2, 5, 3, 3, 4, 5, 4, 3, 2, 6, 4, 3, 6, 2, 5, 6, 4, 2, 5, 4, 5, 1, 1, 1, 4, 4, 2, 3, 6, 6, 5, 5, 4, 3, 5, 5, 2, 2, 1, 3, 6, 1, 5, 2, 6, 5, 4, 3, 4, 6, 6, 5, 5, 6, 1, 5, 6, 6, 3, 3, 1, 5, 4, 5, 1, 5, 2, 2, 4, 3, 4, 2, 1, 6, 1, 3, 2, 4, 1, 3, 5, 3, 1, 3, 2, 6, 2, 5, 1, 3, 6, 2

Offset

1,2

Links

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

Example

G.f.: Let A(x) = x + 6*x^2 + 6*x^3 + 3*x^4 + 4*x^5 + 4*x^6 + ...
then A(x) = B(B(B(B(B(B(x)))))) where B(x) = x + x^2 - 4*x^3 + 28*x^4 - 236*x^5 + 2159*x^6 + ... is the g.f. of A112113.

Prog

(PARI) {a(n, m=6)=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. A112113, A112104-A112111, A112114-A112127.

Sequence in context: A010498 A339083 A240502 * A193085 A338004 A197510

Adjacent sequences: A112109 A112110 A112111 * A112113 A112114 A112115

Keyword

nonn

Author

Paul D. Hanna, Aug 27 2005

Status

approved