A006339

[Emeric Deutsch]

My apologies.
My Maple program answers the following:

David Wilson wrote:
>
> Can someone tell me how to compute, say, the number
> of distinct Pythagorean triangles with hypotenuse 1105?

It gives sequence A046080.
Sorry.
Emeric



On Tue, 17 Jan 2006, Emeric Deutsch wrote:

> On Mon, 16 Jan 2006, David Wilson wrote:
>
>> Someone has asked me how to compute A006339(n), and I've forgotten how.
>> 
>> --------------------------------
>> - David Wilson
>
>
> Here is an elementary (and, therefore, not necessarily the simplest)
> Maple program:
>
> A006339:=proc(n) local ct,x,y: ct:=0: for x from 1 to n-1 do for y from 1 to 
> x do if x^2+y^2=n^2 then ct:=ct+1 else ct:=ct: fi: od: od: ct; end;
>
> The next one will give the legs of the triangles.
>
> b:=proc(n) local P,x,y: P:={}: for x from 1 to n-1 do for y from 1 to x do if 
> x^2+y^2=n^2 then P:=P union {[x,y]} else P:=P: fi: od: od: P; end;
>
> For example, A006339(1105)=13 and
> b(1105)={[884, 663], [817, 744], [1020, 425], [975, 520], [952, 561], [1092, 
> 169], [1071, 272], [1001, 468], [943, 576], [855, 700], [1100, 105], [1104, 
> 47], [1073, 264]}
>
> Of course, the two programs can be combined into one:
>
> a:=proc(n) local P,x,y: P:={}: for x from 1 to n-1 do for y from 1 to x do if 
> x^2+y^2=n^2 then P:=P union {[x,y]} else P:=P: fi: od: od: print(P); nops(P): 
> end;
>
> which gives, for example,
> a(25);
> 		{[20,15],[24,7]}
> 			2
>
> Emeric
>
>
>