A383741 a(0) = 5; a(n) = Pell(5*n)/Pell(n) for n > 0.

5, 29, 1189, 39005, 1332869, 45232349, 1536836005, 52205623709, 1773463509509, 60245500431005, 2046573861616549, 69523263984968669, 2361744412174224005, 80229786688466775389, 2725451003353980465829, 92585104325258634975005, 3145168096067610728884229

Offset: 0

Author

Seiichi Manyama, May 07 2025

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (29,174,-174,-29,1).

Crossrefs

Row n=5 of A383742.

Cf. A000129, A099931.

Programs

Mathematica

a[n_] := Fibonacci[5*n, 2]/Fibonacci[n, 2]; a[0] = 5; Array[a, 17, 0] (* Amiram Eldar, May 08 2025 *)

PARI

my(N=30, x='x+O('x^N)); Vec((5-116*x-522*x^2+348*x^3+29*x^4)/((1-x)*(1+6*x+x^2)*(1-34*x+x^2)))

Formula

a(n) = 29*a(n-1) + 174*a(n-2) - 174*a(n-3) - 29*a(n-4) + a(n-5).

G.f.: (5-116*x-522*x^2+348*x^3+29*x^4)/((1-x) * (1+6*x+x^2) * (1-34*x+x^2)).