A084208 G.f. A(x) defined by: A(x)^8 consists entirely of integer coefficients between 1 and 8 (A083948); A(x) is the unique power series solution with A(0)=1.

1, 1, -3, 15, -82, 484, -2992, 19110, -124979, 832234, -5621028, 38402783, -264858143, 1841221687, -12886279885, 90713376563, -641815393278, 4561172770669, -32542369727538, 232992967457839

Offset

0,3

Comments

Limit a(n)/a(n+1) --> r = -0.131401689761435 where A(r)=0.

Links

Table of n, a(n) for n=0..19.

Mathematica

kmax = 20;
A[x_] = Sum[a[k] x^k, {k, 0, kmax}];
coes = CoefficientList[A[x]^8 + O[x]^(kmax + 1), x];
r = {a[0] -> 1, a[1] -> 1};
coes = coes /. r;
Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 8, 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 *)

Crossrefs

Cf. A083948, A084202-A084207, A084209-A084212.

Sequence in context: A255676 A015680 A371516 * A059271 A345885 A014276

Adjacent sequences: A084205 A084206 A084207 * A084209 A084210 A084211

Keyword

sign

Author

Paul D. Hanna, May 20 2003

Status

approved