A171974 Integer part of the height of a regular tetrahedron with edge length n.

0, 1, 2, 3, 4, 4, 5, 6, 7, 8, 8, 9, 10, 11, 12, 13, 13, 14, 15, 16, 17, 17, 18, 19, 20, 21, 22, 22, 23, 24, 25, 26, 26, 27, 28, 29, 30, 31, 31, 32, 33, 34, 35, 35, 36, 37, 38, 39, 40, 40, 41, 42, 43, 44, 44, 45, 46, 47, 48, 48, 49, 50, 51, 52, 53, 53, 54, 55, 56, 57, 57, 58, 59

Offset: 1

Author

Reinhard Zumkeller, Jan 20 2010

Keywords

• nonn

Comments

-3 <= 4*A171975(n) - 3*a(n) < 3;

a(n)*A171975(n) <= A007590(n);

floor(a(n)*A171971(n)/3) <= A171973(n).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Tetrahedron
• Wikipedia, Tetrahedron
• Index entries for sequences related to Beatty sequences

Crossrefs

Cf. A171972, A022840. Beatty sequence of A157697.

Cf. A007590, A171971, A171973, A171975.

Programs

Haskell

a171974 = floor . (/ 3) . (* sqrt 6) . fromInteger
-- Reinhard Zumkeller, Dec 15 2012

Formula

a(n) = floor(n*sqrt(6)/3).