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%I #11 Jul 30 2017 16:37:32
%S 0,0,2,2,2,2,2,6,6,2,2,20,2,2,20,12,2,6,2,20,20,2,2,56,6,2,12,20,2,20,
%T 2,20,20,2,20,56,2,2,20,56,2,20,2,20,56,2,2,110,6,6,20,20,2,12,20,56,
%U 20,2,2,182,2,2,56,30,20,20,2,20,20,20,2,156,2,2
%N Number of integer Heron triangles of height n.
%H Eric M. Schmidt, <a href="/A221838/b221838.txt">Table of n, a(n) for n = 1..10000</a>
%H Sourav Sen Gupta, Nirupam Kar, Subhamoy Maitra, Santanu Sarkar, and Pantelimon Stanica, <a href="http://www.emis.de/journals/INTEGERS/papers/n3/n3.Abstract.html">Counting Heron triangles with Constraints</a>, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 13, Paper A3, 2013.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle.</a>
%F a(n) = A221837(n) + A046079(n) = A046079(n)^2 + A046079(n).
%e For n = 3, the two triangles have side lengths (3, 4, 5) and (5, 5, 8), with areas 6 and 12 respectively.
%o (Sage) def A221838(n) : pyth = (number_of_divisors(n^2 if n%2==1 else (n/2)^2) - 1) // 2; return pyth^2 + pyth
%Y Cf. A046079, A221837.
%K nonn
%O 1,3
%A _Eric M. Schmidt_, Jan 27 2013