A236533 Number of non-congruent Heronian triangles with base length n whose apex lies on or within a space bounded by a semicircle of diameter n.

0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 1, 2, 0, 0, 3, 1, 0, 0, 2, 3, 2, 0, 0, 2, 5, 0, 1, 0, 2, 2, 0, 4, 0, 4, 5, 2, 2, 0, 2, 3, 0, 0, 4, 0, 4, 6, 6, 3, 0, 1, 2, 0, 3, 0, 8, 2, 0, 2, 1, 8, 1, 0, 4, 1, 4, 0, 2, 5, 6, 9, 0, 1, 5, 0, 8, 0, 4, 0, 2, 9

Offset: 1

Author

Frank M Jackson, Jan 28 2014

Keywords

• nonn

Examples

			a(20)=3 as there are 3 non-congruent Heronian triangles with base length of 20 whose apex lies on or within the space bounded by a semicircle of diameter 20. The integer triples are (7,15,20), (11,13,20), (12,16,20).
		

Crossrefs

Cf. A236384.

Programs

Mathematica

gettriangles[c_] := (s=(a+b+c)/2; area2=s(s-a)(s-b)(s-c); n=0; Do[If[IntegerQ[Sqrt[area2]]&&a+b>c&&a^2+b^2<=c^2, n++], {b, 1, c}, {a, 1, b}]; n); Table[gettriangles[m], {m, 1, 200}]