A112114 Unique sequence of numbers {1,2,3,...,7} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (7th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

1, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 5, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 7, 4, 7, 4, 4, 4, 3, 2, 5, 3, 1, 1, 7, 5, 2, 4, 2, 2, 1, 2, 6, 5, 1, 5, 7, 7, 7, 7, 5, 6, 5, 6, 4, 1, 6, 1, 2, 7, 1, 5, 3, 7, 2, 4, 4, 4, 3, 2, 4, 5, 7, 7, 3, 1, 2, 3, 5, 5, 6, 4, 7, 6, 1, 6, 5, 2, 1, 1, 6, 1, 4, 3, 1, 2, 3, 3, 3, 7, 1

Offset

1,2

Links

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

Example

G.f.: A(x) = x + 7*x^2 + 7*x^3 + 7*x^4 + 7*x^5 + 7*x^6 + 7*x^7 + ...
then A(x) = B(B(B(B(B(B(B(x))))))) where
B(x) = x + x^2 - 5*x^3 + 43*x^4 - 443*x^5 + 4957*x^6 - 57281*x^7 + ...
is the g.f. of A112115.

Prog

(PARI) {a(n, m=7)=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. A112115, A112104-A112113, A112116-A112127.

Sequence in context: A195413 A083947 A269349 * A031182 A106705 A010727

Adjacent sequences: A112111 A112112 A112113 * A112115 A112116 A112117

Keyword

nonn

Author

Paul D. Hanna, Aug 27 2005

Status

approved