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a(n) = number of triangles ABC with side lengths (n, m, p) such that n, m, p are integers, 1 <= n <= m <= p, gcd(n, m, p) = 1, the Nagel point N of ABC lies on the incircle C(I, r).
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%I #6 Oct 26 2019 22:26:44

%S 1,1,1,1,2,1,2,2,3,2,5,2,6,3,4,4,8,3,9,4,6,5,11,4

%N a(n) = number of triangles ABC with side lengths (n, m, p) such that n, m, p are integers, 1 <= n <= m <= p, gcd(n, m, p) = 1, the Nagel point N of ABC lies on the incircle C(I, r).

%C 3*n = m + p.

%e a(1) = 1; degenerate triangle (1, 1, 2).

%e a(2) = 1; triangle (2, 3, 3).

%e a(3) = 1; triangle (3, 4, 5).

%e a(4) = 1; triangle (4, 5, 7).

%e a(5) = 2; triangles (5, 6, 9) and (5, 7, 8).

%K nonn,easy

%O 1,5

%A _Philippe Deléham_, Aug 13 2003