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%I #38 Dec 23 2023 14:27:31
%S 0,1,7,61,511,4309,36295,305773,2575951,21700933,182817943,1540136797,
%T 12974772895,109305051829,920832637543,7757489084749,65352415243759,
%U 550556775723301,4638126412988215,39073566199597117,329172480353038399,2773090156866434197,23361700862301500167
%N Expansion of x/(1 - 7*x - 12*x^2).
%H Vincenzo Librandi, <a href="/A015572/b015572.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 (7,12).
%F a(n) = 7*a(n-1) + 12*a(n-2).
%t a[n_]:=(MatrixPower[{{1,4},{1,-8}},n].{{1},{1}})[[2,1]]; Table[Abs[a[n]],{n,-1,40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2010 *)
%t CoefficientList[Series[x/(1-7x-12x^2),{x,0,30}],x] (* or *) LinearRecurrence[{7,12},{0,1},30] (* _Harvey P. Dale_, Jan 11 2012 *)
%o (Sage) [lucas_number1(n,7,-12) for n in range(0, 20)] # _Zerinvary Lajos_, Apr 24 2009
%o (Magma) [n le 2 select n-1 else 7*Self(n-1) + 12*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 14 2012
%o (PARI) x='x+O('x^30); concat([0], Vec(x/(1-7*x-12*x^2))) \\ _G. C. Greubel_, Jan 06 2018
%K nonn,easy
%O 0,3
%A _Olivier Gérard_
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