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Rounded volume of a regular dodecahedron with edge length n.
5

%I #9 Nov 21 2013 12:47:49

%S 0,8,61,207,490,958,1655,2628,3924,5586,7663,10200,13242,16836,21028,

%T 25863,31388,37649,44691,52561,61305,70968,81597,93237,105935,119736,

%U 134687,150833,168221,186896,206904,228292,251105,275390,301191,328556

%N Rounded volume of a regular dodecahedron with edge length n.

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

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

%F a(n) = round(n^3 * (15+7*sqrt(5))/4)

%e a(6)=1665 because round(6^3*(15+7*sqrt(5))/4)=round(216*7.6631...)=round(1655.23...)=1665.

%t Table[Floor[n^3 (15+7Sqrt[5])/4+1/2],{n,0,50}] (* _Harvey P. Dale_, Apr 25 2011 *)

%o (PARI) for(n=0,100,print1(round(n^3*(15+7*sqrt(5))/4),","))

%Y Cf. A000578 (cube), A071399 (tetrahedron), A071400 (octahedron), A071402 (icosahedron), A071397 (total surface area of dodecahedron).

%K easy,nonn

%O 0,2

%A _Rick L. Shepherd_, May 29 2002