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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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. 84-85.

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.

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

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

AUTHOR

Reinhard Zumkeller, Jan 20 2010

STATUS

approved

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Last modified August 14 07:04 EDT 2020. Contains 336477 sequences. (Running on oeis4.)