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

1,1

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'.

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 *)

Crossrefs

Cf. A120131, A120132, A120133, A055595.

Sequence in context: A331209 A063722 A323058 * A181797 A185152 A028588

Adjacent sequences: A072291 A072292 A072293 * A072295 A072296 A072297

Keyword

nonn

Author

Lekraj Beedassy, Jul 12 2002

Extensions

More terms from Ray Chandler, Jul 02 2004

Status

approved