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A374296 a(n) is the integer part of the area of a regular n-gon whose side lengths are n.

%I A374296 #21 Jul 21 2024 22:27:35
%S A374296 3,16,43,93,178,309,500,769,1133,1612,2228,3005,3969,5147,6570,8268,
%T A374296 10275,12627,15360,18514,22130,26250,30921,36187,42099,48707,56063,
%U A374296 64221,73239,83174,94087,106039,119095,133320,148782,165551,183699,203299
%N A374296 a(n) is the integer part of the area of a regular n-gon whose side lengths are n.
%H A374296 Nicolay Avilov, <a href="/A374296/a374296.jpg">Illustration of a(3)-a(7)</a>
%F A374296 a(n) = floor(n^3/(4*tan(Pi/n))).
%F A374296 a(n) = n^4/(4*Pi) - (Pi/12)*n^2 + O(1). - _Charles R Greathouse IV_, Jul 03 2024
%e A374296 Areas of polygons (starting from n=3):
%e A374296   3.897... (equilateral triangle), so a(3) = 3,
%e A374296  16.000... (square), so a(4) = 16,
%e A374296  43.011... (pentagon), so a(5) = 43,
%e A374296  93.530... (hexagon), so a(6) = 93,
%e A374296 178.061... (heptagon), so a(7) = 178.
%Y A374296 Cf. A064313.
%K A374296 nonn
%O A374296 3,1
%A A374296 _Nicolay Avilov_, Jul 03 2024