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%I #15 Feb 19 2024 11:30:50
%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="http://mathworld.wolfram.com/Octahedron.html">Octahedron</a>
%H Eric Weisstein's World of Mathematics, <a href="http://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
%O 0,2
%A _Rick L. Shepherd_, May 23 2002
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