function tally = collatz1 (ubound)
%
tally = [1 0;2 0];

for ti = 1 : ubound
  
  nums_passed = [];
  tt = ti;
  
  while (tt ~= 1)
    tt = ((mod (tt, 2)) * ((3 * tt) + 1)) + ((1 - mod (tt, 2)) * (tt / 2));
    nums_passed = ([nums_passed tt]);
  end
  
  num_steps = (length (nums_passed));
  
  for tj = 1 : num_steps
    
    idx = find (nums_passed(tj) == tally(:,1));
    if (isempty (idx))
      tally(end+1,:) = [nums_passed(tj) 1];
    else
      tally(idx,2) =  tally(idx,2) + 1;
    end
    
  end

end