function a = Aijn(x,y,i,j,n)
% counting the number of semi-automata
% on n states
% s.t. delta(1,x) = i
% and  delta(1,y) = j
% this is a LOWER BOUND on the real thing

if n==1
  % there is only 1 semi-automaton w/1 state!
  a = 1;
  return
end

if (isempty(x)& ~isempty(y))
  % must have i=1
  % how many n-state semi-automata
  % have delta(1,y) = j ?
  if i>1
    a = 0;
    return
  end
  for k=1:n-1
    ak = Aijn('',y(1:end-1),1,k,n-1);
  end
end
return