A303669 a(n) is the number of lattice points in a Cartesian grid between a circle of radius n, centered at the origin, and an inscribed equilateral triangle; one of the sides of triangle is perpendicular to X-axis.
0, 2, 13, 21, 36, 56, 81, 103, 144, 166, 215, 239, 298, 342, 405, 447, 514, 568, 655, 707, 796, 864, 961, 1019, 1128, 1208, 1337, 1405, 1524, 1614, 1749, 1847, 1990, 2082, 2249, 2333, 2502, 2600, 2789, 2899, 3064, 3192, 3383, 3519, 3718, 3832, 4047, 4175
Offset: 1
Keywords
Examples
For n = 2 we have two lattice points between the defined circle and its inscribed equilateral triangle: (1, 1) and (1, -1).
Links
- Kirill Ustyantsev, Table of n, a(n) for n = 1..1000
- Kirill Ustyantsev, Illustration of this configuration for n=1..10
Programs
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PARI
a(n) = sum(x=-n, +n, sum(y=-n, +n, ((x^2+y^2) < n^2) && ((2*x < - n) || (3*y^2 > (n-x)^2)))); \\ Michel Marcus, May 22 2018
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Python
import math tan=math.sqrt(3)/3 for n in range (1,70): count=0 count1=0 for x in range (-n, n): for y in range (-n,n): if (x*x+y*y