A171973 - OEIS

%I #8 Jul 13 2013 12:03:41

%S 0,0,3,7,14,25,40,60,85,117,156,203,258,323,397,482,579,687,808,942,

%T 1091,1254,1433,1629,1841,2071,2319,2587,2874,3181,3510,3861,4235,

%U 4632,5052,5498,5969,6466,6990,7542,8122,8731,9369,10039,10739,11471,12235

%N Integer part of the volume of a regular tetrahedron with edge length n.

%C Lim{n->oo} a(n)/A000292(n) = sqrt(2)/2;

%C floor(A171971(n)*A171974(n)/3) <= a(n).

%H Reinhard Zumkeller, <a href="/A171973/b171973.txt">Table of n, a(n) for n = 1..1000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetrahedron">Tetrahedron</a>

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

%F a(n) = floor(n^3 * sqrt(2) / 12).

%o (Haskell)

%o a171973 = floor . (/ 12) . (* sqrt 2) . fromInteger . a000578

%o -- _Reinhard Zumkeller_, Dec 15 2012

%Y Cf. A001951, A171972, A171975, A000578.

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Jan 20 2010