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 A360792 #18 Apr 04 2025 22:36:21
%S A360792 0,0,1,2,3,4,5,7,9,10,12,15,17,19,22,25,28,31,34,37,41,45,49,53,57,61,
%T A360792 66,71,75,80,86,91,96,102,108,114,120,126,133,139,146,153,160,167,175,
%U A360792 182,190,198,206,214,223,231,240,249,258,267,276,285,295,305
%N A360792 Integer portion of area of inscribed circle in a regular polygon having n sides of unit length.
%C A360792 Asymptotically equivalent to the area of a circle with circumference n, which is Pi*r^2 with r = n/(2*Pi), thus a(n) ~ n^2 / (4*Pi). (The same follows from taking tan(x) = x in the FORMULA.) Indeed, the integer part of this expression is equal to a(n) or a(n)+1, for all n. - _M. F. Hasler_, Apr 03 2025
%F A360792 a(n) = floor((Pi/4)*(cot(Pi/n)^2)).
%e A360792 For n = 5, the circle inscribed in a regular pentagon with sides of unit length has area (Pi/4)*cot(Pi/5)^2 = 1.4878796365..., so a(5) = floor(1.4878796365...) = 1.
%p A360792 a:= n-> floor(Pi/(2*tan(Pi/n))^2):
%p A360792 seq(a(n), n=3..65); # _Alois P. Heinz_, Feb 20 2023
%t A360792 a[n_] := Floor[(Pi/4)*Cot[Pi/n]^2]; Array[a, 60, 3] (* _Amiram Eldar_, Feb 24 2023 *)
%o A360792 (PARI) a(n) = floor((Pi/4)/tan(Pi/n)^2) \\ _Andrew Howroyd_, Feb 20 2023
%o A360792 (PARI) apply( {A360792(n)=Pi/4\tan(Pi/n)^2}, [3..62]) \\ _M. F. Hasler_, Apr 03 2025
%Y A360792 Cf. A062299, A062300.
%K A360792 nonn
%O A360792 3,4
%A A360792 _A. Timothy Royappa_, Feb 20 2023
%E A360792 More terms from _Andrew Howroyd_, Feb 20 2023