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

3, 16, 43, 93, 178, 309, 500, 769, 1133, 1612, 2228, 3005, 3969, 5147, 6570, 8268, 10275, 12627, 15360, 18514, 22130, 26250, 30921, 36187, 42099, 48707, 56063, 64221, 73239, 83174, 94087, 106039, 119095, 133320, 148782, 165551, 183699, 203299

Offset: 3

Author

Nicolay Avilov, Jul 03 2024

Keywords

• nonn

Examples

			Areas of polygons (starting from n=3):
  3.897... (equilateral triangle), so a(3) = 3,
 16.000... (square), so a(4) = 16,
 43.011... (pentagon), so a(5) = 43,
 93.530... (hexagon), so a(6) = 93,
178.061... (heptagon), so a(7) = 178.
		

Links

• Nicolay Avilov, Illustration of a(3)-a(7)

Crossrefs

Cf. A064313.

Formula

a(n) = floor(n^3/(4*tan(Pi/n))).

a(n) = n^4/(4*Pi) - (Pi/12)*n^2 + O(1). - Charles R Greathouse IV, Jul 03 2024