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A309395 Number of integer-sided triangles with sides a,b,c, max(a,b) < c, a + c = n that are right triangles.

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