A015564 - OEIS

%I #45 Dec 18 2023 12:19:56

%S 0,1,7,55,427,3319,25795,200479,1558123,12109735,94116883,731476591,

%T 5685037435,44184121591,343399075747,2668898259775,20742682272907,

%U 161212165468999,1252941251920435,9737861756257039,75682679805321883

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

%C 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

%H Vincenzo Librandi, <a href="/A015564/b015564.txt">Table of n, a(n) for n = 0..1000</a>

%H Lucyna Trojnar-Spelina and Iwona Włoch, <a href="https://doi.org/10.1007/s40995-019-00757-7">On Generalized Pell and Pell-Lucas Numbers</a>, Iranian Journal of Science and Technology, Transactions A: Science (2019), 1-7.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,6).

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

%t LinearRecurrence[{7, 6}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 14 2012 *)

%o (Sage) [lucas_number1(n,7,-6) for n in range(0, 21)] # _Zerinvary Lajos_, Apr 24 2009

%o (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

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

%K nonn,easy

%O 0,3

%A _Olivier Gérard_