A084207 G.f. A(x) defined by: A(x)^7 consists entirely of integer coefficients between 1 and 7 (A083947); A(x) is the unique power series solution with A(0)=1.

1, 1, -2, 8, -34, 158, -768, 3858, -19851, 104023, -552974, 2973832, -16146688, 88376636, -487034106, 2699839758, -15043262970, 84197804254, -473140314356, 2668221663736, -15095165871964, 85645090974518, -487190919969502

Offset: 0

Author

Paul D. Hanna, May 20 2003

Keywords

• sign

Comments

Limit a(n)/a(n+1) -> r = -0.166670835025545 where A(r)=0.

Crossrefs

Cf. A083947, A084202-A084206, A084208-A084212.

Programs

Mathematica

kmax = 25;
A[x_] = Sum[a[k] x^k, {k, 0, kmax}];
coes = CoefficientList[A[x]^7 + O[x]^(kmax + 1), x];
r = {a[0] -> 1, a[1] -> 1};
coes = coes /. r;
Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 7, a[k-1], Integers] // ToRules];
coes = coes /. r, {k, 3, kmax + 1}];
Table[a[k], {k, 0, kmax}] /. r (* Jean-François Alcover, Jul 26 2018 *)