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A171970
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Integer part of the height of an equilateral triangle with side length n.
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6
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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)
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OFFSET
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1,3
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=1..73.
Eric Weisstein's World of Mathematics, Equilateral Triangle
Wikipedia, Equilateral triangle
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FORMULA
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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).
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PROG
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(PARI) a(n)=sqrtint(3*n^2\4) \\ Charles R Greathouse IV, Jan 06 2013
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Reinhard Zumkeller, Jan 20 2010
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STATUS
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approved
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