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 A137212 #23 Jan 02 2024 08:58:13
%S A137212 0,0,1,5,20,72,245,805,2584,8160,25465,78773,242060,740040,2253581,
%T A137212 6841525,20719600,62629632,189025585,569820965,1716088004,5164258440,
%U A137212 15531389285,46687390213,140287229320,421405027680,1265526821161
%N A137212 a(n) = 5*a(n-1) - 5*a(n-2) - 3*a(n-3).
%H A137212 G. C. Greubel, <a href="/A137212/b137212.txt">Table of n, a(n) for n = 0..1000</a>
%H A137212 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,-3).
%F A137212 a(n) = A193519(n)/2.
%F A137212 From _R. J. Mathar_, Mar 17 2008: (Start)
%F A137212 O.g.f.: x^2/((1-3*x)*(1-2*x-x^2)).
%F A137212 a(n) = (3^n - A078057(n))/2 . (End)
%F A137212 a(n) = (1/4)*(2*3^n - A002203(n+1)). - _G. C. Greubel_, Jan 05 2022
%t A137212 LinearRecurrence[{5,-5,-3},{0,0,1},30] (* _Harvey P. Dale_, Nov 28 2013 *)
%o A137212 (Magma) [n le 3 select Floor((n-1)/2) else 5*Self(n-1) -5*Self(n-2) -3*Self(n-3): n in [1..31]]; // _G. C. Greubel_, Jan 05 2022
%o A137212 (Sage) [(2*3^n - lucas_number2(n+1, 2, -1))/4 for n in (0..30)] # _G. C. Greubel_, Jan 05 2022
%Y A137212 Cf. A002203, A078057, A193519.
%K A137212 nonn,easy
%O A137212 0,4
%A A137212 _Paul Curtz_, Mar 06 2008