A071396 - OEIS

%I #16 Feb 16 2025 08:32:46

%S 0,3,14,31,55,87,125,170,222,281,346,419,499,585,679,779,887,1001,

%T 1122,1251,1386,1528,1677,1833,1995,2165,2342,2525,2716,2913,3118,

%U 3329,3547,3772,4005,4244,4489,4742,5002,5269,5543,5823,6111,6405,6707,7015,7330

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

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

%H Vincenzo Librandi, <a href="/A071396/b071396.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Octahedron.html">Octahedron</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PlatonicSolid.html">Platonic Solid</a>

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

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

%t Table[Round[2n^2 Sqrt[3]],{n,0,50}] (* _Harvey P. Dale_, Feb 19 2024 *)

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

%o (Magma) [Round(2*n^2 * Sqrt(3)): n in [0..50]]; // _Vincenzo Librandi_, May 21 2011

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

%K easy,nonn,changed

%O 0,2

%A _Rick L. Shepherd_, May 23 2002