A015603 - OEIS

%I #32 Sep 22 2025 16:00:24

%S 0,1,11,130,1529,17989,211640,2489941,29294111,344644690,4054738589,

%T 47703926689,561235840880,6602929589881,77683348056611,

%U 913943194931650,10752525276757649,126503266798718989,1488308662276727720,17509924686232475821

%N a(n) = 11*a(n-1) + 9*a(n-2).

%H Vincenzo Librandi, <a href="/A015603/b015603.txt">Table of n, a(n) for n = 0..900</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,9).

%F G.f.: x/(1 - 11*x - 9*x^2). - _Zerinvary Lajos_, Apr 27 2009

%t Join[{a=0,b=1},Table[c=11*b+9*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 31 2011 *)

%t LinearRecurrence[{11, 9}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 22 2012 *)

%o (SageMath) [lucas_number1(n,11,-9) for n in range(0, 18)] # _Zerinvary Lajos_, Apr 27 2009

%o (Magma) [n le 2 select n-1 else 11*Self(n-1) + 9*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 22 2012

%o (PARI) x='x+O('x^30); concat([0], Vec(x/(1-11*x-9*x^2))) \\ _G. C. Greubel_, Jan 16 2018

%K nonn,easy

%O 0,3

%A _Olivier Gérard_

%E G.f. adapted to the offset by _Vincenzo Librandi_, Nov 22 2012