A171973 Integer part of the volume of a regular tetrahedron with edge length n.

0, 0, 3, 7, 14, 25, 40, 60, 85, 117, 156, 203, 258, 323, 397, 482, 579, 687, 808, 942, 1091, 1254, 1433, 1629, 1841, 2071, 2319, 2587, 2874, 3181, 3510, 3861, 4235, 4632, 5052, 5498, 5969, 6466, 6990, 7542, 8122, 8731, 9369, 10039, 10739, 11471, 12235

Offset: 1

Author

Reinhard Zumkeller, Jan 20 2010

Keywords

• nonn

Comments

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

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Wikipedia, Tetrahedron
• Eric Weisstein's World of Mathematics, Tetrahedron

Crossrefs

Cf. A001951, A171972, A171975, A000578.

Programs

Haskell

a171973 = floor . (/ 12) . (* sqrt 2) . fromInteger . a000578
-- Reinhard Zumkeller, Dec 15 2012

Formula

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