This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A071396 #20 Jun 06 2025 03:29:11
%S A071396 0,3,14,31,55,87,125,170,222,281,346,419,499,585,679,779,887,1001,
%T A071396 1122,1251,1386,1528,1677,1833,1995,2165,2342,2525,2716,2913,3118,
%U A071396 3329,3547,3772,4005,4244,4489,4742,5002,5269,5543,5823,6111,6405,6707,7015,7330
%N A071396 Rounded total surface area of a regular octahedron with edge length n.
%D A071396 S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, pp. 10-11.
%H A071396 Vincenzo Librandi, <a href="/A071396/b071396.txt">Table of n, a(n) for n = 0..10000</a>
%H A071396 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Octahedron.html">Octahedron</a>
%H A071396 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PlatonicSolid.html">Platonic Solid</a>
%F A071396 a(n) = round(2 * n^2 * sqrt(3)).
%e A071396 a(3)=31 because round(2*3^2*sqrt(3)) = round(18*1.73205...) = round(31.1769...) = 31.
%t A071396 Table[Round[2n^2 Sqrt[3]],{n,0,50}] (* _Harvey P. Dale_, Feb 19 2024 *)
%o A071396 (PARI) for(n=0,100,print1(round(2*n^2*sqrt(3)),","))
%o A071396 (Magma) [Round(2*n^2 * Sqrt(3)): n in [0..50]]; // _Vincenzo Librandi_, May 21 2011
%o A071396 (Python)
%o A071396 from math import isqrt
%o A071396 def A071396(n): return (m:=isqrt(k:=3*n**4<<2))+int(k>m*(m+1)) # _Chai Wah Wu_, Jun 05 2025
%Y A071396 Cf. A070169 (tetrahedron), A033581 (cube), A071397 (dodecahedron), A071398 (icosahedron), A071400 (volume of octahedron).
%K A071396 easy,nonn
%O A071396 0,2
%A A071396 _Rick L. Shepherd_, May 23 2002