This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A127213 #17 Jan 20 2024 16:07:16
%S A127213 6,108,864,9072,85536,839808,8118144,78941952,765904896,7437339648,
%T A127213 72196614144,700923912192,6804621582336,66060990332928,
%U A127213 641332318961664,6226189565755392,60445100877152256,586813429630107648
%N A127213 a(n) = 6^n*Lucas(n), where Lucas = A000204.
%H A127213 G. C. Greubel, <a href="/A127213/b127213.txt">Table of n, a(n) for n = 1..1000</a>
%H A127213 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,36).
%F A127213 a(n) = Trace of matrix [({6,6},{6,0})^n].
%F A127213 a(n) = 6^n * Trace of matrix [({1,1},{1,0})^n].
%F A127213 From _Colin Barker_, Sep 02 2013: (Start)
%F A127213 a(n) = 6*a(n-1) + 36*a(n-2).
%F A127213 G.f.: -6*x*(12*x+1)/(36*x^2+6*x-1). (End)
%t A127213 Table[6^n Tr[MatrixPower[{{1, 1}, {1, 0}}, x]], {x, 1, 20}]
%t A127213 Table[6^n*LucasL[n], {n,1,50}] (* _G. C. Greubel_, Dec 18 2017 *)
%t A127213 LinearRecurrence[{6,36},{6,108},20] (* _Harvey P. Dale_, Jan 20 2024 *)
%o A127213 (PARI) x='x+O('x^30); Vec(-6*x*(12*x+1)/(36*x^2+6*x-1)) \\ _G. C. Greubel_, Dec 18 2017
%o A127213 (Magma) [6^n*Lucas(n): n in [1..30]]; // _G. C. Greubel_, Dec 18 2017
%Y A127213 Cf. A000204, A087131, A127210, A127211, A127212, A127214, A127215, A127216.
%K A127213 nonn,easy
%O A127213 1,1
%A A127213 _Artur Jasinski_, Jan 09 2007