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A171970 Integer part of the height of an equilateral triangle with side length n. 6


%S 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,

%T 23,24,25,25,26,27,28,29,30,31,32,32,33,34,35,36,37,38,38,39,40,41,42,

%U 43,44,45,45,46,47,48,49,50,51,51,52,53,54,55,56,57,58,58,59,60,61,62,63

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

%D Mohammad K. Azarian, A Trigonometric Characterization of Equilateral Triangle, Problem 336, Mathematics and Computer Education, Vol. 31, No. 1, Winter 1997, p. 96. Solution published in Vol. 32, No. 1, Winter 1998, pp. 84-85.

%D Mohammad K. Azarian, Equating Distances and Altitude in an Equilateral Triangle, Problem 316, Mathematics and Computer Education, Vol. 28, No. 3, Fall 1994, p. 337. Solution published in Vol. 29, No. 3, Fall 1995, pp. 324-325.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EquilateralTriangle.html">Equilateral Triangle</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Equilateral_triangle">Equilateral triangle</a>

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

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

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

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

%o (PARI) a(n)=sqrtint(3*n^2\4) \\ _Charles R Greathouse IV_, Jan 06 2013

%Y Beatty sequence of A010527.

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

%K nonn,easy

%O 1,3

%A _Reinhard Zumkeller_, Jan 20 2010

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Last modified September 30 20:19 EDT 2020. Contains 337440 sequences. (Running on oeis4.)