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

1,3

Links

Table of n, a(n) for n=1..73.

Eric Weisstein's World of Mathematics, Equilateral Triangle

Wikipedia, Equilateral triangle

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).

Prog

(PARI) a(n)=sqrtint(3*n^2\4) \\ Charles R Greathouse IV, Jan 06 2013
(Python)
from math import isqrt
def A171970(n): return isqrt(3*n*n>>2) # Chai Wah Wu, Jun 12 2026

Crossrefs

Beatty sequence of A010527.

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

Sequence in context: A145569 A213851 A172475 * A071377 A076946 A302780

Adjacent sequences: A171967 A171968 A171969 * A171971 A171972 A171973

Keyword

nonn,easy,changed

Author

Reinhard Zumkeller, Jan 20 2010

Status

approved