A343946 Surface area of a right prism whose base is a regular n-gon with unit side length and unit height (rounded to the nearest integer).

4, 6, 8, 11, 14, 18, 21, 25, 30, 34, 39, 45, 50, 56, 62, 69, 76, 83, 91, 99, 107, 115, 124, 133, 142, 152, 162, 173, 183, 194, 206, 217, 229, 242, 254, 267, 281, 294, 308, 322, 337, 352, 367, 382, 398, 414, 431, 447, 464, 482, 500, 518, 536, 555, 574, 593, 612, 632, 653

Offset: 3

Author

Wesley Ivan Hurt, May 04 2021

Keywords

• nonn

Examples

			a(3) = 4; the surface area of a right prism whose base is an equilateral triangle with unit side lengths and height is 3+sqrt(3)/2 = 3.8660..., which rounds up to 4.
a(4) = 6 (surface area of a cube with unit side length and height).
		

Links

• Wikipedia, Prism (geometry)

Crossrefs

Cf. A134030 (volume).

Programs

Mathematica

Table[Round[n + n*Cot[Pi/n]/2], {n, 3, 100}]

Formula

a(n) = round(n+n*cot(Pi/n)/2).