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%I #16 Jan 22 2018 03:12:30
%S 1,3,5,11,18,29,44,70,94,136,177,243,303,386,485,611,738,914,1093,
%T 1312,1529,1831,2114,2488,2854,3310,3756,4307,4880,5520,6187,6995,
%U 7800,8738,9674,10797,11875,13161,14437,15901,17388,19087,20797,22706,24618,26811
%N a(n) is the number of triangles (up to congruence) with integer coordinates that have perimeter strictly less than n.
%H Peter Kagey, <a href="/A298121/b298121.txt">Table of n, a(n) for n = 4..150</a>
%H Peter Kagey, <a href="https://codegolf.stackexchange.com/q/153106/53884">Integer Triangles with perimeter less than n</a>, Programming Puzzles & Code Golf Stack Exchange.
%F a(n) = Sum_{k=3..n-1} A298079(k).
%e All a(7) = 11 triangles with integer coordinates and perimeter less than 7 are congruent to triangles with coordinates:
%e (0, 0), (0, 1), (1, 0) - with perimeter ~3.41; or
%e (0, 0), (1, 2), (0, 1) - with perimeter ~4.65; or
%e (0, 0), (0, 2), (1, 1) - with perimeter ~4.82; or
%e (0, 0), (0, 2), (1, 0) - with perimeter ~5.23; or
%e (0, 0), (1, 2), (2, 1) - with perimeter ~5.88; or
%e (0, 0), (2, 2), (0, 1) - with perimeter ~6.06; or
%e (0, 0), (1, 3), (0, 1) - with perimeter ~6.39; or
%e (0, 0), (0, 2), (2, 1) - with perimeter ~6.47; or
%e (0, 0), (1, 3), (0, 2) - with perimeter ~6.57; or
%e (0, 0), (0, 3), (1, 1) - with perimeter ~6.65; or
%e (0, 0), (0, 2), (2, 0) - with perimeter ~6.82.
%Y Cf. A298079.
%K nonn
%O 4,2
%A _Peter Kagey_, Jan 12 2018
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