A298121 a(n) is the number of triangles (up to congruence) with integer coordinates that have perimeter strictly less than n.

1, 3, 5, 11, 18, 29, 44, 70, 94, 136, 177, 243, 303, 386, 485, 611, 738, 914, 1093, 1312, 1529, 1831, 2114, 2488, 2854, 3310, 3756, 4307, 4880, 5520, 6187, 6995, 7800, 8738, 9674, 10797, 11875, 13161, 14437, 15901, 17388, 19087, 20797, 22706, 24618, 26811

Offset: 4

Author

Peter Kagey, Jan 12 2018

Keywords

• nonn

Examples

			All a(7) = 11 triangles with integer coordinates and perimeter less than 7 are congruent to triangles with coordinates:
(0, 0), (0, 1), (1, 0) - with perimeter ~3.41; or
(0, 0), (1, 2), (0, 1) - with perimeter ~4.65; or
(0, 0), (0, 2), (1, 1) - with perimeter ~4.82; or
(0, 0), (0, 2), (1, 0) - with perimeter ~5.23; or
(0, 0), (1, 2), (2, 1) - with perimeter ~5.88; or
(0, 0), (2, 2), (0, 1) - with perimeter ~6.06; or
(0, 0), (1, 3), (0, 1) - with perimeter ~6.39; or
(0, 0), (0, 2), (2, 1) - with perimeter ~6.47; or
(0, 0), (1, 3), (0, 2) - with perimeter ~6.57; or
(0, 0), (0, 3), (1, 1) - with perimeter ~6.65; or
(0, 0), (0, 2), (2, 0) - with perimeter ~6.82.
		

Links

• Peter Kagey, Table of n, a(n) for n = 4..150
• Peter Kagey, Integer Triangles with perimeter less than n, Programming Puzzles & Code Golf Stack Exchange.

Crossrefs

Cf. A298079.

Formula

a(n) = Sum_{k=3..n-1} A298079(k).