My code is making a random LED generator using LSFR. But, I want to turn on only one LED at a time, but my program is randomly generating 1-3 LED at a time.

There are a couple of issues.. check out this code and try if it works.. this is the correct way to implement a LFSR.

`timescale 1ns/1ns
module Memorygame 
	(
	   input wire       clk, 
	   input wire       rst_n, 
	   output reg [3:0] out
  	); 
 
integer   count;
reg       clk_1hz;
wire     lf;  // linear feedback of XORed bits.
 
always @ (posedge clk or negedge rst_n) begin // slows our clock from 50mhz to 1hz 
  if(!rst_n)  begin
    count = 0;
    clk_1hz <= 1'b0;
  end
  else begin
    if (count<250000)
      count <= count + 1; 
    else begin 
      clk_1hz <= ~clk_1hz;
      count <= 0;
    end 
  end 
end //always
 
assign lf =  !(out[3] ^ out[0]);
always @(posedge clk_1hz or negedge rst_n) begin
   if(!rst_n)
     out <= 4'b0000;
   else begin
     out <= {out[2],out[1],
             out[0], lf}; 
    end
end //always