A303706 - OEIS

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

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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