A171970 Integer part of the height of an equilateral triangle with side length n.

0, 1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 12, 12, 13, 14, 15, 16, 17, 18, 19, 19, 20, 21, 22, 23, 24, 25, 25, 26, 27, 28, 29, 30, 31, 32, 32, 33, 34, 35, 36, 37, 38, 38, 39, 40, 41, 42, 43, 44, 45, 45, 46, 47, 48, 49, 50, 51, 51, 52, 53, 54, 55, 56, 57, 58, 58, 59, 60, 61, 62, 63

Offset: 1

Author

Reinhard Zumkeller, Jan 20 2010

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, Equilateral Triangle
• Wikipedia, Equilateral triangle

Crossrefs

Beatty sequence of A010527.

Cf. A022838, A004526, A005843, A171971, A171972.

Programs

PARI

a(n)=sqrtint(3*n^2\4) \\ Charles R Greathouse IV, Jan 06 2013

Formula

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

a(n) = floor(A022838(n)/2).

a(n)*A004526(n) <= A171971(n)

a(n)*A005843(n) <= A171972(n).