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A338201 a(n) is the number of unit perimeter triangles with rational side lengths whose largest denominator is equal to n.

%I A338201 #22 Nov 09 2020 21:35:51
%S A338201 0,0,1,0,1,0,2,1,2,1,4,2,5,2,5,4,8,4,10,8,10,6,14,8,15,9,16,14,21,13,
%T A338201 24,16,23,16,41,18,33,20,33,32,40,32,44,34,53,30,52,32,54,35,54,48,65,
%U A338201 38,87,70,67,49,80,64,85,56,116,64,116,73,102,80,96,99
%N A338201 a(n) is the number of unit perimeter triangles with rational side lengths whose largest denominator is equal to n.
%C A338201 Records occur at n=1, 3, 7, 11, 13, 17, 19, 23, 25, 27, 29, 31, 35, 43, 45, 49, 53, 55, 63, 73, 75, 77, 91, 99, 105, 117, 133, 143, 175, 187, ...
%H A338201 Peter Kagey, <a href="/A338201/b338201.txt">Table of n, a(n) for n = 1..300</a>
%H A338201 Code Golf Stack Exchange, <a href="https://codegolf.stackexchange.com/q/213646/53884">Triangles with rational side lengths</a>
%H A338201 Peter Kagey, <a href="/A338201/a338201.txt">Haskell program</a>.
%e A338201 For n = 20, the a(20) = 8 triangles have sides:
%e A338201 1/4,  7/20, 2/5;
%e A338201 1/12, 9/20, 7/15;
%e A338201 3/10, 7/20, 7/20;
%e A338201 3/20, 2/5,  9/20;
%e A338201 1/4,  3/10, 9/20;
%e A338201 2/15, 5/12, 9/20;
%e A338201 1/5,  7/20, 9/20; and
%e A338201 1/10, 9/20, 9/20.
%Y A338201 Cf. A180360, A338202.
%K A338201 nonn
%O A338201 1,7
%A A338201 _Peter Kagey_, Oct 16 2020