A084208 - OEIS

%I #6 Jul 26 2018 18:43:43

%S 1,1,-3,15,-82,484,-2992,19110,-124979,832234,-5621028,38402783,

%T -264858143,1841221687,-12886279885,90713376563,-641815393278,

%U 4561172770669,-32542369727538,232992967457839

%N 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.

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

%t kmax = 20;

%t A[x_] = Sum[a[k] x^k, {k, 0, kmax}];

%t coes = CoefficientList[A[x]^8 + O[x]^(kmax + 1), x];

%t r = {a[0] -> 1, a[1] -> 1};

%t coes = coes /. r;

%t Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 8, a[k-1], Integers] // ToRules];

%t coes = coes /. r, {k, 3, kmax + 1}];

%t Table[a[k], {k, 0, kmax}] /. r (* _Jean-François Alcover_, Jul 26 2018 *)

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

%K sign

%O 0,3

%A _Paul D. Hanna_, May 20 2003