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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

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: A060999 A089187 A179178 * A253895 A004006 A089240

Adjacent sequences:  A171970 A171971 A171972 * A171974 A171975 A171976

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jan 20 2010

STATUS

approved

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Last modified June 28 05:07 EDT 2017. Contains 288813 sequences.