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A171973 Integer part of the volume of a regular tetrahedron with edge length n. 8
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
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
Sequence in context: A316319 A368205 A179178 * A253895 A365641 A004006
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jan 20 2010
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)