A015564 Expansion of x/(1 - 7*x - 6*x^2).

0, 1, 7, 55, 427, 3319, 25795, 200479, 1558123, 12109735, 94116883, 731476591, 5685037435, 44184121591, 343399075747, 2668898259775, 20742682272907, 161212165468999, 1252941251920435, 9737861756257039, 75682679805321883

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Comments

Pisano period lengths: 1, 1, 1, 1, 12, 1, 4, 2, 3, 12, 15, 1, 168, 4, 12, 4, 288, 3, 18, 12, ... - R. J. Mathar, Aug 10 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Lucyna Trojnar-Spelina and Iwona Włoch, On Generalized Pell and Pell-Lucas Numbers, Iranian Journal of Science and Technology, Transactions A: Science (2019), 1-7.
• Index entries for linear recurrences with constant coefficients, signature (7,6).

Programs

Magma

[n le 2 select n-1 else 7*Self(n-1) + 6*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2012

Mathematica

LinearRecurrence[{7, 6}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)
CoefficientList[Series[x/(1-7x-6x^2),{x,0,20}],x] (* Harvey P. Dale, Dec 04 2024 *)

PARI

x='x+O('x^30); concat([0], Vec(x/(1-7*x-6*x^2))) \\ G. C. Greubel, Dec 30 2017

Sage

[lucas_number1(n,7,-6) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009

Formula

a(n) = 7*a(n-1) + 6*a(n-2).