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Expansion of x/(1 - 3*x - 11*x^2).
11

%I #34 Aug 19 2024 23:12:57

%S 0,1,3,20,93,499,2520,13049,66867,344140,1767957,9089411,46715760,

%T 240130801,1234265763,6344236100,32609631693,167615492179,

%U 861552425160,4428427689449,22762359745107,116999783819260,601385308653957,3091153547973731

%N Expansion of x/(1 - 3*x - 11*x^2).

%H Vincenzo Librandi, <a href="/A015529/b015529.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 (3,11).

%F a(n) = 3*a(n-1) + 11*a(n-2).

%F a(n) = -22^n*(A^n - B^n)/sqrt(53) where A = -1/(3+sqrt(53)) and B = 1/(sqrt(53)-3). - _R. J. Mathar_, Apr 29 2008

%t Join[{a=0,b=1},Table[c=3*b+11*a;a=b;b=c,{n,100}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 16 2011 *)

%t LinearRecurrence[{3, 11}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 12 2012 *)

%t CoefficientList[Series[x/(1-3x-11x^2),{x,0,30}],x] (* _Harvey P. Dale_, Aug 19 2024 *)

%o (Sage) [lucas_number1(n,3,-11) for n in range(0, 22)] # _Zerinvary Lajos_, Apr 22 2009

%o (Magma) [n le 2 select n-1 else 3*Self(n-1) + 11*Self(n-2): n in [1..30] ]; // _Vincenzo Librandi_, Nov 12 2012

%o (PARI) x='x+O('x^30); concat([0], Vec(x/(1-3*x-11*x^2))) \\ _G. C. Greubel_, Jan 01 2018

%K nonn,easy

%O 0,3

%A _Olivier GĂ©rard_