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A171971 Integer part of the area of an equilateral triangle with side length n. 6
0, 1, 3, 6, 10, 15, 21, 27, 35, 43, 52, 62, 73, 84, 97, 110, 125, 140, 156, 173, 190, 209, 229, 249, 270, 292, 315, 339, 364, 389, 416, 443, 471, 500, 530, 561, 592, 625, 658, 692, 727, 763, 800, 838, 876, 916, 956, 997, 1039, 1082, 1126, 1170, 1216, 1262, 1309 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The Beatty sequence of sqrt(3)/4 starts 0, 0, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7,... for n>=1. This sequence here subsamples the Beatty sequence at the positions of the squares. - R. J. Mathar, Dec 02 2012

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Wikipedia, Equilateral triangle

Eric Weisstein's World of Mathematics, Equilateral Triangle

FORMULA

a(n) = floor(n^2 * sqrt(3) / 4).

a(n)*A171974(n)/3 <= A171973(n);

A171970(n)*A004526(n) <= a(n).

PROG

(Haskell)

a171971 = floor . (/ 4) . (* sqrt 3) . fromInteger . a000290

-- Reinhard Zumkeller, Dec 15 2012

(PARI) a(n)=sqrtint(3*n^4\16) \\ Charles R Greathouse IV, Apr 08 2013

CROSSREFS

Cf. A171972, A022838, A000290.

Sequence in context: A033439 A194082 A061786 * A184009 A105334 A130486

Adjacent sequences:  A171968 A171969 A171970 * A171972 A171973 A171974

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jan 20 2010

STATUS

approved

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Last modified October 2 05:40 EDT 2014. Contains 247537 sequences.