

A343946


Surface area of a right prism whose base is a regular ngon 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
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OFFSET

3,1


LINKS



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



KEYWORD

nonn


AUTHOR



STATUS

approved



