A239246 Number of primitive Heronian triangles with n as greatest side length.

0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 3, 0, 0, 2, 2, 0, 0, 1, 3, 2, 0, 1, 2, 3, 0, 0, 0, 0, 2, 1, 5, 0, 4, 3, 4, 1, 0, 2, 1, 0, 0, 2, 0, 2, 4, 6, 4, 0, 2, 2, 0, 2, 0, 1, 3, 0, 1, 0, 8, 2, 0, 5, 1, 2, 0, 0, 6, 2, 7, 0, 3, 0, 0, 3, 0, 2, 0, 0, 9

Offset

1,13

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Heronian Triangle.

Example

a(17)=3 as there are 3 primitive Heronian triangles with greatest side length of 17. They are (9, 10, 17), (8, 15, 17) and (16, 17, 17).

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, c]]], {c, 3, nn}, {b, c}, {a, b}]; Table[Length@Select[lst, #==n &], {n, 1, nn}] (* using T. D. Noe's program at A083875 *)

Crossrefs

Cf. A054875, A070138, A096467, A123323, A134587.

Sequence in context: A226171 A284280 A278520 * A171700 A162660 A324848

Adjacent sequences: A239243 A239244 A239245 * A239247 A239248 A239249

Keyword

nonn

Author

Frank M Jackson, Mar 13 2014

Status

approved