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A298121
a(n) is the number of triangles (up to congruence) with integer coordinates that have perimeter strictly less than n.
2
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, 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 * A373273 A244473 A023597
KEYWORD
nonn
AUTHOR
Peter Kagey, Jan 12 2018
STATUS
approved