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

1,15

Links

Table of n, a(n) for n=1..85.

Example

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).

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}]

Crossrefs

Cf. A236384.

Sequence in context: A058087 A240753 A202149 * A298187 A298183 A098356

Adjacent sequences: A236530 A236531 A236532 * A236534 A236535 A236536

Keyword

nonn

Author

Frank M Jackson, Jan 28 2014

Status

approved