A376900 a(n) is the number of distinct integer-sided right triangles that can be drawn into a square with side length n.

0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 5, 6, 6, 6, 6, 8, 10, 10, 10, 11, 11, 11, 11, 13, 13, 14, 14, 17, 17, 17, 18, 18, 18, 18, 19, 20, 21, 23, 25, 25, 25, 25, 27, 27, 27, 27, 29, 31, 31, 31, 34, 34, 34, 34, 37, 37, 37, 37, 40, 41, 42, 43, 43, 45, 45, 46

Offset: 0

Author

Felix Huber, Oct 25 2024

Keywords

• nonn

Examples

			a(11) = 3 because exactly the 3 integer-sided right triangles (3, 4, 5), (6, 8, 10), (5, 12, 13) can be drawn into a square with side length 11.
See linked Maple program to calculate the right triangles for a given n.
		

Links

• Felix Huber, Table of n, a(n) for n = 0..10000
• Felix Huber, Maple program to calculate the right triangles for a given n

Crossrefs

Cf. A009012.

Programs

Maple

A376900:=proc(n)
   local a,p,q,v,k;
   a:=0;
      for p from 2 to evalf(sqrt(sqrt(2)*n+1)) do
         for q from 1 to min(p-1,floor(n/(sqrt(2)*p))) do
            if gcd(p,q)=1 and is(p+q,odd) then
               v:=max(p^2-q^2,2*p*q);
               k:=min(p^2-q^2,2*p*q)/v;
               a:=a+floor(n/v*sqrt(k^2-2*k+2));
            fi;
         od;
      od;
   return a;
end proc;
seq(A376900(n),n=0..70);