module triples
  implicit none

  integer :: max_peri, prim, total
  integer :: u(9,3) = reshape((/ 1, -2, 2,  2, -1, 2,  2, -2, 3, &
                                 1,  2, 2,  2,  1, 2,  2,  2, 3, &
                                -1,  2, 2, -2,  1, 2, -2,  2, 3 /), &
                                (/ 9, 3 /))

contains

recursive subroutine new_tri(in)
  integer, intent(in) :: in(:)
  integer :: i
  integer :: t(3), p

  p = sum(in)
  if (p > max_peri) return

  prim = prim + 1
  total = total + max_peri / p
  do i = 1, 3
    t(1) = sum(u(1:3, i) * in)
    t(2) = sum(u(4:6, i) * in)
    t(3) = sum(u(7:9, i) * in)
    call new_tri(t);
  end do
end subroutine new_tri
end module triples

program Pythagorean
  use triples
  implicit none

  integer :: seed(3) = (/ 3, 4, 5 /)

  max_peri = 10
  do
    total = 0
    prim = 0
    call new_tri(seed)
    write(*, "(a, i10, 2(i10, a))") "Up to", max_peri, total, " triples",  prim, " primitives"
    if(max_peri == 100000000) exit
    max_peri = max_peri * 10
  end do
end program Pythagorean