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

3,1

Links

Table of n, a(n) for n=3..61.

Wikipedia, Prism (geometry)

Formula

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

Example

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).

Mathematica

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

Crossrefs

Cf. A134030 (volume).

Sequence in context: A226250 A075325 A026278 * A293806 A310661 A351415

Adjacent sequences: A343943 A343944 A343945 * A343947 A343948 A343949

Keyword

nonn

Author

Wesley Ivan Hurt, May 04 2021

Status

approved