%I #14 Sep 08 2022 08:45:06
%S 0,2,17,59,140,273,471,748,1117,1590,2182,2904,3770,4793,5987,7363,
%T 8936,10719,12724,14964,17454,20205,23231,26545,30160,34089,38345,
%U 42942,47893,53209,58906,64995,71490,78404,85749,93540,101789,110509
%N Rounded volume of a regular icosahedron with edge length n.
%C The printed reference given shows in a table on p. 10 that Volume is "2.18170a^3" (a is edge). Both PARI (see Example here) and a handheld calculator show that 2.18169 is correct for a 5-decimal-place approximation.
%D S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, pp. 10-11.
%H Vincenzo Librandi, <a href="/A071402/b071402.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Icosahedron.html">Icosahedron</a>
%F a(n) = round(n^3 * (3+sqrt(5)) * 5/12).
%e a(6)=471 because round(6^3*(3 + sqrt(5))*5/12) = round(216*2.181694990...) = round(471.24...) = 471.
%o (PARI) for(n=0,100,print1(round(n^3*(3+sqrt(5))*5/12),","))
%o (Magma) [Round(n^3 * (3+Sqrt(5)) * 5/12): n in [0..50]]; // _Vincenzo Librandi_, May 21 2011
%Y Cf. A000578 (cube), A071399 (tetrahedron), A071400 (octahedron), A071401 (dodecahedron), A071398 (total surface area of icosahedron).
%Y Cf. A102208 ((3+Sqrt(5)) * 5/12).
%K easy,nonn
%O 0,2
%A _Rick L. Shepherd_, May 29 2002