A171973 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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).