Triangles with given inradius, A057721

[Hugo Pfoertner]

Jud McCranie wrote:
> 
> At 02:42 PM 6/11/2006, Hugo Pfoertner wrote:
> |   Number of all possible triangles
> >|   |  Pythagorean triangles
> >1   1  1
> >2   5  2
> >3  13  3
> >4  18  3
> >5  15  3
> >6  45  6
> >[...]
> >
> >Thanks to Jud McCranie for checking up to triangle side lengths 2000;
> >his results confirm the correctness of 1,5,13,18,15,... and also that
> >the longest side for inradius 6 is A057721(6)=1405.
> 
> And if that equation for the longest side is correct (and it is too good to
> be false!) then the next term is 24 (after 1, 5, 13, 18, 15, 45).

In the meantime Thomas Mautsch seems to have found more terms. In a post
to de.sci.mathematik

http://groups.google.com/group/de.sci.mathematik/msg/39d8cf3d20360949

he gave

1,5,13,18,15,45,24,45,51,52,26,139,

which I fed into superseeker and got:

Betreff: Reply from superseeker
Datum: Sun, 11 Jun 2006 18:34:43 -0400 (EDT)
Von: superseq-re... at research.att.com
An: noth... at abouthugo.de

Report on [ 15,45,24,45,51,52,26,139]:
[...]
        SUCCESS
Transformation T007 gave a match with:
%I A007237 M3878
%S A007237 5,18,45,45,52,139,80,89,184,145,103,312,96,225,379
%N A007237 Number of triangles with integer sides and area = n times
perimeter.
%D A007237 Problem E3408, Amer. Math. Monthly, 99 (1992), 175-176.
...
%K A007237 nonn
%O A007237 1,1
%A A007237 Simon Plouffe (plouffe(AT)math.uqam.ca)

List of transformations used:
T007  elements of even index in the sequence

i.e. A120062(2*n)=A007237(n)

Hugo