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

1,3

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

Formula

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

Prog

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

Crossrefs

Cf. A001951, A171972, A171975, A000578.

Sequence in context: A316319 A368205 A179178 * A253895 A365641 A004006

Adjacent sequences: A171970 A171971 A171972 * A171974 A171975 A171976

Keyword

nonn

Author

Reinhard Zumkeller, Jan 20 2010

Status

approved