A391073 - OEIS

%I #10 Dec 16 2025 08:45:14

%S 0,0,0,1,0,0,1,0,0,1,0,0,1,1,0,3,0,1,1,0,0,1,0,0,1,1,1,1,0,1,3,0,0,1,

%T 1,0,1,0,0,4,0,0,1,0,0,3,0,0,1,0,1,4,1,0,1,0,0,1,1,0,3,1,0,1,0,3,1,0,

%U 1,1,0,0,1,1,0,6,0,0,4,0,0,1,0,0,1,2,0,3

%N a(n) is the number of nondegenerate triangles (n, n + d, n + 2*d) with integer area for some nonnegative integers d.

%C d < n because n + 2*d < n + (n + d).

%H Felix Huber, <a href="/A391073/b391073.txt">Table of n, a(n) for n = 0..10000</a>

%e The a(15) = 3 triangles are (15, 20, 25) with d = 5 and area 150, (15, 26, 37) with d = 11 and area 156, (15, 28, 41) with d = 13 and area 126.

%p A391073 := proc(n) local b, c, d, x; c := 0; for d to n - 1 do x := 3*(n + d)^2*(n + 3*d)*(n - d); if irem(x, 16) = 0 then x := 1/16*x; b := isqrt(x); if b*b = x then c := c + 1; end if; end if; end do; c; end proc: seq(A391073(n), n = 1 .. 88);

%Y Cf. A024164, A336750, A351178, A379663, A387908.

%K nonn

%O 0,16

%A _Felix Huber_, Dec 09 2025