A171971 Integer part of the area of an equilateral triangle with side length n.

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

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

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).

Mathematica

Table[Floor[(n^2 Sqrt[3])/4], {n, 60}] (* Harvey P. Dale, Apr 13 2022 *)

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,changed

Author

Reinhard Zumkeller, Jan 20 2010

Status

approved