(* Frieze pattern recursion with "square" initial conditions *)
Clear[x]
x[i_,0]:=x[i]
x[0,j_]:=x[-j]
x[i_,j_]:=x[i,j]=Expand[Simplify[(x[i-1,j] x[i,j-1]+1)/x[i-1,j-1]]]

(* List of monomials of a Laurent polynomial *)
monoms=Apply[List,#]&

(* List of exponents in each monomial *)
xm[i_,j_]:=Map[Table[Exponent[#,x[k]],{k,-j,i}]&,monoms[x[i,j]]]

(* Print them nicely *)
TableForm[xm[4,4]]

(* Create output files *)
wx[i_,j_, channel_]:=Block[
    {m = xm[i,j]},
    Map[
      (* write one row *)
      (Map[
            WriteString[channel,Switch[#,1,"+",-1,"-",0,"."]]&,#];
          WriteString[channel,"\n"])&,
      m]
    ]
Do[Block[{s=OpenWrite["frieze-"<>ToString[n]<>"-"<>ToString[n]<>".mon"]},
    wx[n,n,s];Close[s]],{n,1,6}]