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

4,2

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.

Formula

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

Example

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.

Crossrefs

Cf. A298079.

Sequence in context: A267030 A128949 A070316 * A244473 A023597 A281357

Adjacent sequences: A298118 A298119 A298120 * A298122 A298123 A298124

Keyword

nonn

Author

Peter Kagey, Jan 12 2018

Status

approved