Because the grid is really small, we can just simulate the process of a cow jumping from the top-left corner to the bottom-right corner. We start at the top-left corner and recursively try all squares both to the bottom and to the right of the current square that are a different color from the square that we're in. Here is my Java code showing this.

import java.io.*;
import java.util.*;

public class barnjump {
  static char[][] grid;

  public static void main(String[] args) throws IOException {
    BufferedReader br = new BufferedReader(new FileReader("barnjump.in"));
    PrintWriter pw = new PrintWriter(new BufferedWriter(new FileWriter("barnjump.out")));
    StringTokenizer st = new StringTokenizer(br.readLine());

    int r = Integer.parseInt(st.nextToken());
    int c = Integer.parseInt(st.nextToken());

    /* Read the input into the grid array. */
    grid = new char[r][c];
    for(int i = 0; i < r; i++) {
      String s = br.readLine();
      for(int j = 0; j < c; j++) {
        grid[i][j] = s.charAt(j);
      }
    }

    /* Compute the answer! */
    pw.println(count(0,0));
    pw.close();
  }
  
  public static int count(int x, int y) {
    if(x == grid.length-1 && y == grid[x].length-1) {
      /* We arrived at the destination. */
      return 1;
    }

    /* Otherwise try all valid next moves and sum the total number of paths. */
    int ret = 0;
    for(int i = x+1; i < grid.length; i++) {
      for(int j = y+1; j < grid[i].length; j++) {
        if(grid[i][j] != grid[x][y]) {
          ret += count(i, j);
        }
      }
    }
    return ret;
  }
}