

A171970


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


6



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
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OFFSET

1,3


COMMENTS

a(n) = floor(A022838(n)/2);
a(n)*A004526(n) <= A171971(n);
a(n)*A005843(n) <= A171972(n).


REFERENCES

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. 8485.
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. 324325.


LINKS

Table of n, a(n) for n=1..73.
Wikipedia, Equilateral triangle
Eric Weisstein's World of Mathematics, Equilateral Triangle


FORMULA

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


PROG

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


CROSSREFS

Beatty sequence of A010527.
Sequence in context: A145569 A213851 A172475 * A071377 A076946 A302780
Adjacent sequences: A171967 A171968 A171969 * A171971 A171972 A171973


KEYWORD

nonn,easy


AUTHOR

Reinhard Zumkeller, Jan 20 2010


STATUS

approved



