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 A259821 #36 Sep 30 2024 19:05:41
%S A259821 4,5,11,29,83,245,731,2189,6563,19685,59051,177149,531443,1594325,
%T A259821 4782971,14348909,43046723,129140165,387420491,1162261469,3486784403,
%U A259821 10460353205,31381059611,94143178829,282429536483
%N A259821 a(n) = floor( (3^n+1)^2/3^n ).
%C A259821 a(n) is the curvature (rounded down) of circles inscribed between a unit circle and a circumscribed equilateral triangle. See illustration.
%C A259821 Apart from the first term the same as A168607. - _R. J. Mathar_, Jul 09 2015
%H A259821 Colin Barker, <a href="/A259821/b259821.txt">Table of n, a(n) for n = 0..1000</a>
%H A259821 Kival Ngaokrajang, <a href="/A259821/a259821.pdf">Illustration of initial terms</a>
%H A259821 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F A259821 a(n) = floor( A034472(n)^2/A000244(n) ).
%F A259821 From _Colin Barker_, Jul 07 2015: (Start)
%F A259821 a(n) = 3^n + 2 for n>0.
%F A259821 a(n) = 4*a(n-1) - 3*a(n-2) for n>2.
%F A259821 G.f.: (3*x^2-11*x+4) / ((x-1)*(3*x-1)).
%F A259821 (End)
%t A259821 Table[Floor[(3^n + 1)^2/3^n], {n, 0, 30}] (* _Michael De Vlieger_, Jul 07 2015 *)
%t A259821 LinearRecurrence[{4,-3},{4,5,11},30] (* _Harvey P. Dale_, Sep 30 2024 *)
%o A259821 (PARI)
%o A259821 a(n)=floor((3^n+1)^2/3^n)
%o A259821 for (n=0, 100, print1(a(n),", "))
%o A259821 (PARI) Vec((3*x^2-11*x+4)/((x-1)*(3*x-1)) + O(x^100)) \\ _Colin Barker_, Jul 07 2015
%Y A259821 Cf. A034472, A000244, A168607.
%K A259821 nonn,easy,less
%O A259821 0,1
%A A259821 _Kival Ngaokrajang_, Jul 07 2015