The On-Line Encyclopedia of Integer Sequences (OEIS)

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A303706 revision #27

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

(list; graph; refs; listen; history; text; internal format)

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