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 A171971 Integer part of the area of an equilateral triangle with side length n. 8
 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 Eric Weisstein's World of Mathematics, Equilateral Triangle Wikipedia, Equilateral triangle FORMULA a(n) = floor(n^2 * sqrt(3) / 4) = A308358(n^2). 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 A249736 Adjacent sequences:  A171968 A171969 A171970 * A171972 A171973 A171974 KEYWORD nonn AUTHOR Reinhard Zumkeller, Jan 20 2010 STATUS approved

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Last modified August 12 11:44 EDT 2020. Contains 336439 sequences. (Running on oeis4.)