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

0,2

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

Formula

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

Example

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

Mathematica

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

Prog

(PARI) for(n=0, 100, print1(round(2*n^2*sqrt(3)), ", "))
(Magma) [Round(2*n^2 * Sqrt(3)): n in [0..50]]; // Vincenzo Librandi, May 21 2011

Crossrefs

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

Sequence in context: A014696 A235137 A197944 * A032525 A294420 A197946

Adjacent sequences: A071393 A071394 A071395 * A071397 A071398 A071399

Keyword

easy,nonn

Author

Rick L. Shepherd, May 23 2002

Status

approved