procedure TForm1.tr1Change(Sender: TObject);
var d0,d1: Double;
    Q,N: Integer;
begin
 // 170111 x = (4NQ-Q^2+2Q-1)/(4N-Q^2-2Q+3)
 Q:=tr1.Position;
 cht1.Series[0].Clear;
 cht1.Series[1].Clear; edt1.Text:='';
 for N:=Q+1 to Q+100 do
  begin
   d0:=(4*N*Q-Q*Q+2*Q-1);
   d1:=(4*N-Q*Q-2*Q+3);
   if Abs(d1)<1e-4 then Continue;
   d0:=d0/d1;
   if d0<0 then Continue;
   cht1.Series[0].AddXY(N,d0);
   if Abs(d0-Round(d0))<1e-5 then
    begin
     cht1.Series[1].AddXY(N,d0);
     edt1.Text:=edt1.Text+Format(' N=%d',[N]);
    end;
  end;
 lbl1.Caption:=Format('Q=%d',[Q])
end;