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 A015580 Expansion of x/(1 - 9*x - 4*x^2). 3

%I

%S 0,1,9,85,801,7549,71145,670501,6319089,59553805,561260601,5289560629,

%T 49851088065,469818035101,4427766668169,41729172153925,

%U 393273616058001,3706379233137709,34930507562471385,329200084994793301,3102522795203025249,29239505496806400445

%N Expansion of x/(1 - 9*x - 4*x^2).

%C Pisano period lengths: 1, 1, 2, 1, 3, 2, 48, 2, 6, 3, 10, 2, 42, 48, 6, 4, 24, 6,360, 3, ... - _R. J. Mathar_, Aug 10 2012

%H Vincenzo Librandi, <a href="/A015580/b015580.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,4)

%F a(n) = 9*a(n-1) + 4*a(n-2).

%F a(n) = (1/97)*sqrt(97)*{[(9/2) + (1/2)*sqrt(97)]^n - [(9/2) - (1/2)*sqrt(97)]^n}, with n>=0. - _Paolo P. Lava_, Jan 13 2009

%t Join[{a=0,b=1},Table[c=9*b+4*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 27 2011 *)

%t LinearRecurrence[{9, 4}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 14 2012 *)

%o (Sage) [lucas_number1(n,9,-4) for n in range(0, 19)] # _Zerinvary Lajos_, Apr 26 2009

%o (MAGMA) [n le 2 select n-1 else 9*Self(n-1) + 4*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 14 2012

%o (PARI) x='x+O('x^30); concat([0], Vec(x/(1-9*x-4*x^2))) \\ _G. C. Greubel_, Jan 06 2018

%Y Cf. A015579, A099371.

%K nonn,easy,changed

%O 0,3