A015591 - OEIS

%I #41 Dec 18 2023 10:06:21

%S 0,1,10,109,1180,12781,138430,1499329,16239160,175885561,1905008050,

%T 20633050549,223475577940,2420453234341,26215812544870,

%U 283942204557769,3075364358481520,33309123425835121,360769513484684890,3907477245679364989,42321698078155813900

%N Expansion of x/(1 - 10*x - 9*x^2).

%C Pisano period lengths:  1, 2, 1, 4, 4, 2, 48, 8, 1, 4, 10, 4, 84, 48, 4, 16, 272, 2, 360, 4, ... - _R. J. Mathar_, Aug 10 2012

%H Vincenzo Librandi, <a href="/A015591/b015591.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 (10,9).

%F a(n) = 10*a(n-1) + 9*a(n-2).

%F a(n) = (-3*i)^(n-1) * ChebyshevU(n-1, -5*i/3). - _G. C. Greubel_, Feb 13 2021

%t Join[{a=0,b=1},Table[c=10*b+9*a;a=b;b=c,{n,40}]] (* _Vladimir Joseph Stephan Orlovsky_, Mar 29 2011 *)

%t LinearRecurrence[{10, 9}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 15 2012 *)

%t Table[(-3 I)^(n - 1)*ChebyshevU[n - 1, 5 I/3], {n, 0, 30}] (* _G. C. Greubel_, Feb 13 2021 *)

%o (Sage) [lucas_number1(n,10,-9) for n in range(0, 18)] # _Zerinvary Lajos_, Apr 26 2009

%o (Magma) [n le 2 select n-1 else 10*Self(n-1) + 9*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 15 2012

%Y Cf. A254600.

%K nonn,easy

%O 0,3

%A _Olivier Gérard_

%E Extended by _T. D. Noe_, May 23 2011