A084209 -id:A084209 - cp's OEIS frontend

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

Paul D. Hanna, May 20 2003

sign

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

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

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 *)

A084210 G.f. A(x) defined by: A(x)^10 consists entirely of integer coefficients between 1 and 10 (A083950); A(x) is the unique power series solution with A(0)=1.

Original entry on oeis.org

1, 1, -4, 25, -173, 1292, -10105, 81565, -673691, 5662878, -48263038, 415950272, -3617999891, 31714089336, -279828926113, 2483097203637, -22143011361045, 198317403322755

Offset: 0

Paul D. Hanna, May 20 2003

sign

Limit a(n)/a(n+1) --> r = -0.104430987675729 where A(r)=0.

Cf. A083950, A084202-A084209, A084211, A084212.

kmax = 20;
A[x_] = Sum[a[k] x^k, {k, 0, kmax}];
coes = CoefficientList[A[x]^10 + O[x]^(kmax + 1), x];
r = {a[0] -> 1, a[1] -> 1};
coes = coes /. r;
Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 10, 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 *)

cp's OEIS Frontend

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.

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