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a(n) = 12*a(n-1) + 5*a(n-2) for n >= 2, a(0) = 0, a(1) = 1.
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%I #35 Dec 23 2023 14:27:43

%S 0,1,12,149,1848,22921,284292,3526109,43734768,542447761,6728046972,

%T 83448802469,1035025864488,12837554386201,159225781956852,

%U 1974897155413229,24494894774743008,303813223073982241,3768233150761501932,46737863924507934389

%N a(n) = 12*a(n-1) + 5*a(n-2) for n >= 2, a(0) = 0, a(1) = 1.

%H Vincenzo Librandi, <a href="/A015610/b015610.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 (12,5).

%F G.f.: x/(1 - 12*x - 5*x^2). - _Vincenzo Librandi_, Nov 22 2012

%t Join[{a=0,b=1},Table[c=12*b+5*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 31 2011 *)

%t CoefficientList[Series[x/(1 - 12x - 5x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{12, 5}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 22 2012 *)

%o (Sage) [lucas_number1(n,12,-5) for n in range(0, 18)] # _Zerinvary Lajos_, Apr 29 2009

%o (Magma) [n le 2 select n-1 else 12*Self(n-1) + 5*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 22 2012

%o (PARI) x='x+O('x^30); concat([0], Vec(x/(1-12*x-5*x^2))) \\ _G. C. Greubel_, Dec 30 2017

%K nonn,easy

%O 0,3

%A _Olivier GĂ©rard_