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A171971
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Integer part of the area of an equilateral triangle with side length n.
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6
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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
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 1..1000
Wikipedia, Equilateral triangle
Eric Weisstein's World of Mathematics, Equilateral Triangle
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FORMULA
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a(n) = floor(n^2 * sqrt(3) / 4).
a(n)*A171974(n)/3 <= A171973(n);
A171970(n)*A004526(n) <= a(n).
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PROG
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(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
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CROSSREFS
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Cf. A171972, A022838, A000290.
Sequence in context: A033439 A194082 A061786 * A184009 A105334 A130486
Adjacent sequences: A171968 A171969 A171970 * A171972 A171973 A171974
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KEYWORD
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nonn
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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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