A071396 Rounded total surface area of a regular octahedron with edge length n.

0, 3, 14, 31, 55, 87, 125, 170, 222, 281, 346, 419, 499, 585, 679, 779, 887, 1001, 1122, 1251, 1386, 1528, 1677, 1833, 1995, 2165, 2342, 2525, 2716, 2913, 3118, 3329, 3547, 3772, 4005, 4244, 4489, 4742, 5002, 5269, 5543, 5823, 6111, 6405, 6707, 7015, 7330

Offset: 0

Author

Rick L. Shepherd, May 23 2002

Keywords

• easy
• nonn

Examples

			a(3)=31 because round(2*3^2*sqrt(3)) = round(18*1.73205...) = round(31.1769...) = 31.
		

References

• S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, pp. 10-11.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Octahedron
• Eric Weisstein's World of Mathematics, Platonic Solid

Crossrefs

Cf. A070169 (tetrahedron), A033581 (cube), A071397 (dodecahedron), A071398 (icosahedron), A071400 (volume of octahedron).

Programs

Magma

[Round(2*n^2 * Sqrt(3)): n in [0..50]]; // Vincenzo Librandi, May 21 2011

Mathematica

Table[Round[2n^2 Sqrt[3]],{n,0,50}] (* Harvey P. Dale, Feb 19 2024 *)

PARI

for(n=0,100,print1(round(2*n^2*sqrt(3)),","))

Python

from math import isqrt
def A071396(n): return (m:=isqrt(k:=3*n**4<<2))+int(k>m*(m+1)) # Chai Wah Wu, Jun 05 2025

Formula

a(n) = round(2 * n^2 * sqrt(3)).