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%I #13 Feb 01 2021 21:23:38
%S 1,2,1,3,3,2,1,1,1,1,1,2,1,5,2,5,1,1,2,1,1,1,2,2,1,1,2,1,7,5,3,1,5,1,
%T 1,5,3,1,2,1,1,1,1,1,2,3,1,1,5,1,4,1,1,1,8,5,1,3,2,1,1,1,3,6,3,2,2,3,
%U 2,1,1,2,1,3,3,4,1,1,1,3,1,2,1,3,4,2,2,1,1,7,1,2,7,1,1
%N Number of Heronian triangles with perimeter A335103(n) whose smallest side length is a square.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Heronian_triangle">Heronian triangle</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>
%F a(n) = Sum_{k=1..floor(b(n)/3)} Sum_{i=k..floor((b(n)-k)/2)} sign(floor((i+k)/(b(n)-i-k+1))) * chi(sqrt((b(n)/2)*(b(n)/2-i)*(b(n)/2-k)*(b(n)/2-(b(n)-i-k)))) * c(k), where chi(n) = 1 - ceiling(n) + floor(n), c is the square characteristic (A010052) and b = A335103.
%e a(1) = 1; There is one Heronian triangle with perimeter A335103(1) = 32 whose smallest side length is a square, [4,13,15].
%Y Cf. A010052, A335103, A335208, A335211.
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, May 26 2020
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