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%I #15 Sep 08 2022 08:45:06
%S 0,21,83,186,330,516,743,1012,1321,1672,2065,2498,2973,3489,4047,4645,
%T 5285,5967,6689,7453,8258,9105,9993,10922,11892,12904,13957,15051,
%U 16186,17363,18581,19841,21141,22483,23866,25291,26757,28264,29812
%N Rounded total surface area of a regular dodecahedron with edge length n.
%D S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, pp. 10-11.
%H Vincenzo Librandi, <a href="/A071397/b071397.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Dodecahedron.html">Dodecahedron</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PlatonicSolid.html">Platonic Solid</a>
%F a(n) = round(3 * n^2 * sqrt(25 + 10*sqrt(5))).
%e a(4)=330 because round(3*4^2*sqrt(25 + 10*sqrt(5))) = round(48*6.88190...) = round(330.331...) = 330.
%t With[{c=3*Sqrt[25+10*Sqrt[5]]},Round[c*Range[0,40]^2]] (* _Harvey P. Dale_, Jul 06 2018 *)
%o (PARI) for(n=0,100,print1(round(3*n^2*sqrt(25+10*sqrt(5))),","))
%o (Magma) [Round(3 * n^2 * Sqrt(25+10*Sqrt(5))): n in [0..50]]; // _Vincenzo Librandi_, May 21 2011
%Y Cf. A070169 (tetrahedron), A033581 (cube), A071396 (octahedron), A071398 (icosahedron), A071401 (volume of dodecahedron).
%K easy,nonn
%O 0,2
%A _Rick L. Shepherd_, May 28 2002
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