A115065 Number of points with integer coordinates inside the equilateral triangle with base [0,n].

1, 2, 4, 6, 10, 14, 20, 26, 33, 40, 49, 58, 69, 80, 93, 106, 120, 134, 150, 166, 184, 202, 222, 242, 263, 284, 307, 330, 355, 380, 406, 432, 460, 488, 518, 548, 580, 612, 645, 678, 713, 748, 785, 822, 861, 900, 940, 980, 1022

Offset: 0

Author

Neven Juric (neven.juric(AT)apis-it.hr), Jun 20 2006

Keywords

• nonn

Comments

If one replaces the equilateral triangle by a rectangle isoscele triangle with hypotenuse [0,n], one gets A087811. - Michel Marcus, Aug 05 2013

Examples

			For n=0, the triangle is degenerate and there is 1 point (0,0).
For n=1, there are 2 points (0,0) and (0,1).
		

Programs

PARI

a(n) = {nb = 0; for (x=0, n, for (y=0, n, if ((x < n/2) && (y <= x*sqrt(3)), nb++); if ((x >= n/2) && (y + x*sqrt(3)) <= n*sqrt(3), nb++););); nb;} \\ Michel Marcus, Aug 05 2013

Extensions

Offset set to 0 and a(0) prepended by Michel Marcus, Aug 05 2013