A015575 Expansion of x/(1 - 8*x - 5*x^2).

0, 1, 8, 69, 592, 5081, 43608, 374269, 3212192, 27568881, 236612008, 2030740469, 17428983792, 149585572681, 1283829500408, 11018563866669, 94567658435392, 811634086816481, 6965910986708808, 59785458327752869, 513113221555566992, 4403833064083300281, 37796230620444237208

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Comments

Pisano period lengths: 1, 2, 3, 2, 4, 6, 21, 4, 9, 4, 120, 6, 56, 42, 12, 8, 16, 18, 360, 4, ... - R. J. Mathar, Aug 10 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,5).

Programs

Magma

[n le 2 select n-1 else 8*Self(n-1) + 5*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2012

Mathematica

Join[{a=0,b=1},Table[c=8*b+5*a;a=b;b=c,{n,100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011 *)
LinearRecurrence[{8, 5}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)
CoefficientList[Series[x/(1-8x-5x^2),{x,0,30}],x] (* Harvey P. Dale, Feb 28 2023 *)

PARI

x='x+O('x^30); concat([0], Vec(x/(1-8*x-5*x^2))) \\ G. C. Greubel, Jan 06 2018

Sage

[lucas_number1(n,8,-5) for n in range(0, 20)] # Zerinvary Lajos, Apr 25 2009

Formula

a(n) = 8*a(n-1) + 5*a(n-2).