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%I #9 Feb 25 2015 17:25:27
%S 0,0,1,3,8,15,25,40,60,86,118,157,204,259,323,398,483,579,687,808,943,
%T 1091,1255,1434,1629,1841,2071,2320,2587,2874,3182,3511,3862,4235,
%U 4632,5053,5498,5970,6467,6991,7542,8122,8731,9370,10039,10739,11471,12236
%N Rounded volume of a regular tetrahedron 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/Tetrahedron.html">Tetrahedron</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PlatonicSolid.html">Platonic Solid</a>
%F a(n) = round(n^3 * sqrt(2)/12)
%e a(4)=8 because round(4^3*sqrt(2)/12)=round(64*.11785...)=round(7.542...)=8.
%t With[{c=Sqrt[2]/12},Round[c*Range[0,50]^3]] (* _Harvey P. Dale_, Feb 25 2015 *)
%o (PARI) for(n=0,100,print1(round(n^3*sqrt(2)/12),","))
%Y Cf. A000578 (cube), A071400 (octahedron), A071401 (dodecahedron), A071402 (icosahedron), A070169 (total surface area of tetrahedron).
%K easy,nonn
%O 0,4
%A _Rick L. Shepherd_, May 29 2002
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