The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #14 Feb 24 2023 16:38:35
%S 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 66,71,75,80,86,91,96,102,108,114,120,126,133,139,146,153,160,167,175,
%U 182,190,198,206,214,223,231,240,249,258,267,276,285,295,305
%N Integer portion of area of inscribed circle in a regular polygon having n sides of unit length.
%F a(n) = floor((Pi/4)*(cot(Pi/n)^2)).
%e 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 a:= n-> floor(Pi/(2*tan(Pi/n))^2):
%p seq(a(n), n=3..65); # _Alois P. Heinz_, Feb 20 2023
%t a[n_] := Floor[(Pi/4)*Cot[Pi/n]^2]; Array[a, 60, 3] (* _Amiram Eldar_, Feb 24 2023 *)
%o (PARI) a(n) = floor((Pi/4)/tan(Pi/n)^2) \\ _Andrew Howroyd_, Feb 20 2023
%Y Cf. A062299, A062300.
%K nonn
%O 3,4
%A _A. Timothy Royappa_, Feb 20 2023
%E More terms from _Andrew Howroyd_, Feb 20 2023