|
|
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.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|