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Expansion of x/(1 - 5*x - 12*x^2).
5

%I #38 Dec 30 2023 23:41:04

%S 0,1,5,37,245,1669,11285,76453,517685,3505861,23741525,160777957,

%T 1088788085,7373275909,49931836565,338138493733,2289874507445,

%U 15507034462021,105013666399445,711152745541477,4815927724500725,32613471569001349

%N Expansion of x/(1 - 5*x - 12*x^2).

%H Vincenzo Librandi, <a href="/A015548/b015548.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 (5,12).

%F a(n) = 2*A099919(n-1) + 1, for n>=1.

%F a(n) = 5 a(n-1) + 12 a(n-2).

%t Join[{a=0,b=1},Table[c=5*b+12*a;a=b;b=c,{n,100}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 16 2011 *)

%t LinearRecurrence[{5, 12}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 13 2012 *)

%t CoefficientList[Series[x/(1-5x-12x^2),{x,0,30}],x] (* _Harvey P. Dale_, May 27 2023 *)

%o (Sage) [lucas_number1(n,5,-12) for n in range(0, 21)] # _Zerinvary Lajos_, Apr 24 2009

%o (Magma) [n le 2 select n-1 else 5*Self(n-1) + 12*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 13 2012

%o (PARI) x='x+O('x^30); concat([0], Vec(x/(1-5*x-12*x^2))) \\ _G. C. Greubel_, Jan 16 2018

%Y Cf. A015564 (binom. transf.)

%K nonn,easy

%O 0,3

%A _Olivier GĂ©rard_