A015532 a(n) = 4*a(n-1) + 7*a(n-2).

0, 1, 4, 23, 120, 641, 3404, 18103, 96240, 511681, 2720404, 14463383, 76896360, 408829121, 2173591004, 11556167863, 61439808480, 326652408961, 1736688295204, 9233320043543, 49090098240600, 260993633267201, 1387605220753004, 7377376315882423

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Comments

Pisano period lengths: 1, 2, 8, 4, 4, 8, 3, 4, 24, 4, 110, 8, 168, 6, 8, 8, 288, 24, 18, 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 (4,7).

Programs

Magma

[n le 2 select n-1 else 4*Self(n-1)+7*Self(n-2): n in [1..30] ]; // Vincenzo Librandi, Nov 12 2012

Mathematica

a[n_]:=(MatrixPower[{{1,2},{1,-5}},n].{{1},{1}})[[2,1]]; Table[Abs[a[n]],{n,-1,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)
LinearRecurrence[{4, 7}, {0, 1}, 30] (* Vincenzo Librandi, Nov 12 2012 *)

PARI

x='x+O('x^30); concat([0], Vec(x/(1-4*x-7*x^2))) \\ G. C. Greubel, Jan 01 2018

Sage

[lucas_number1(n,4,-7) for n in range(0, 21)]# Zerinvary Lajos, Apr 23 2009

Formula

From R. J. Mathar, Apr 29 2008: (Start)

O.g.f.: x/(1 - 4*x - 7*x^2).

a(n) = -7^n*(A^n - B^n)/(2*sqrt(11)) where A = -1/(2+sqrt(11)) and B = 1/(sqrt(11)-2). (End)