|
|
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
|
|
LINKS
|
|
|
FORMULA
|
a(n) = floor(n^2 * sqrt(3) / 4) = A308358(n^2).
|
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|