A303706 a(n) is the number of lattice points in a Cartesian grid between an equilateral triangle and an inscribed circle of radius n; one of the side of triangle is perpendicular to the X-axis; the circle's center is at the origin.

0, 5, 14, 29, 42, 65, 94, 123, 154, 187, 234, 289, 328, 383, 436, 507, 572, 645, 716, 789, 884, 961, 1058, 1159, 1244, 1347, 1454, 1573, 1692, 1805, 1940, 2057, 2194, 2325, 2454, 2621, 2758, 2927, 3060, 3221, 3404, 3571, 3746, 3909, 4086, 4293, 4478, 4677, 4868, 5061, 5256, 5465, 5698, 5915

Offset

1,2

Links

Table of n, a(n) for n=1..54.

Kirill Ustyantsev, Geometric illustration

Example

For n = 2 we have 5 lattice points: (-1, 2); (-1, -2); (2, -1); (2, 1); (3, 0).

Prog

(Python)
import math
tan=math.sqrt(3)/3
for n in range (1, 71):
  count=0
  for x in range (-n, 2*n):
   for y in range (-2*n, 2*n):
    if (x*x+y*y>n*n and y<-tan*x+2*tan*n and y>tan*x-2*tan*n and x>-n):
     count=count+1
  print(count)
(PARI) a(n) = sum(x=-n+1, 2*n, sum(y=-2*n, 2*n, ((x^2+y^2) > n^2) && (3*y^2 < (x-2*n)^2))); \\ Michel Marcus, May 22 2018

Crossrefs

Cf. A303644, A303646.

Sequence in context: A212678 A244100 A031333 * A161437 A301681 A047801

Adjacent sequences: A303703 A303704 A303705 * A303707 A303708 A303709

Keyword

nonn

Author

Kirill Ustyantsev, Apr 29 2018

Status

approved