%I #18 Jul 30 2019 21:07:42
%S 0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,2,0,0,0,0,0,1,2,0,1,0,0,0,0,3,0,0,
%T 0,2,0,0,0,1,0,0,0,0,1,0,0,1,3,4,0,0,0,2,0,1,0,0,0,0,0,0,1,3,0,0,0,0,
%U 0,0,0,5,0,0,2,0,0,0,0,1,4,0,0,0,0,0,0,1,0,2,0,0,0,0,0,3,0,6,1,4
%N Number of integer-sided triangles with sides a,b,c, max(a,b) < c, a + c = n that are right triangles.
%H Seiichi Manyama, <a href="/A309395/b309395.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) > 0 if and only if n is a term in A046790.
%F a(n^2) = floor((n-1)/2) = A004526(n-1).
%e n | (a,b,c)
%e -----+-----------------------------------------
%e 8 | [ 3, 4, 5]
%e 9 | [ 4, 3, 5]
%e 16 | [ 6, 8, 10]
%e 18 | [ 5, 12, 13], [ 8, 6, 10]
%e 24 | [ 9, 12, 15]
%e 25 | [ 8, 15, 17], [12, 5, 13]
%e 27 | [12, 9, 15]
%e 32 | [ 7, 24, 25], [12, 16, 20], [15, 8, 17]
%e 36 | [10, 24, 26], [16, 12, 20]
%o (PARI) {a(n) = sum(k=n\2+1, n-1, issquare(k^2-(n-k)^2))}
%Y Cf. A004526, A024155, A046790, A082523.
%K nonn
%O 1,18
%A _Seiichi Manyama_, Jul 28 2019