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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). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,1
LINKS
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 04 2021
STATUS
approved

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Last modified June 16 14:12 EDT 2024. Contains 373430 sequences. (Running on oeis4.)