A072294 Areas of primitive Heronian triangles sorted by longest side, then by middle side and finally shortest side.

6, 12, 12, 30, 60, 24, 84, 36, 60, 120, 66, 42, 84, 126, 60, 90, 84, 168, 36, 204, 210, 210, 60, 120, 132, 72, 84, 252, 360, 114, 156, 180, 210, 420, 120, 210, 420, 168, 420, 240, 468, 126, 180, 336, 360, 420, 264, 330, 252, 168, 504, 420, 780, 420, 306, 456, 156

Offset: 1

Author

Lekraj Beedassy, Jul 12 2002

Keywords

• nonn

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000 (first 2197 terms from Zak Seidov)
• A. Dendane, Heron's Formula for Area of a Triangle-Geometry Calculator
• Zak Seidov, Table of n=1..6093, A072294(n), A120131(n), A120132(n), A120133(n) (with A120131(n) <=1000)
• Michael Somos, Heronian Triangle Table
• P. Yiu, Heron triangles with sides < 100 Appendix Chap. 9.3 pp. 81/360 in 'Recreational Mathematics'.

Crossrefs

Cf. A120131, A120132, A120133, A055595.

Programs

Mathematica

nn = 200; lst = {}; Do[s = (a + b + c)/2; If[IntegerQ[s] && GCD[a, b, c] == 1, area2 = s (s - a) (s - b) (s - c); If[area2 > 0 && IntegerQ[Sqrt[area2]], AppendTo[lst, Sqrt[area2]]]], {a, nn}, {b, a}, {c, b}]; lst (* T. D. Noe, Mar 23 2011 *)

Extensions

More terms from Ray Chandler, Jul 02 2004