def path_counter(x,y): path = {} #generate path[list] for matrix x*y path[x,y] = 0 # matrix 0 if(x==1 and y==1): return 0 # matrix 1 if(x==1 or y==1): return 1 # path of the horizontal and vertical border for coor_x in range(x-1,0,-1): path[coor_x,y] = 1 for coor_y in range(y-1,0,-1): path[x,coor_y] = 1 # loop to fill path of all other note for coor_x in range(x-1,0,-1): for coor_y in range(y-1,0,-1): path[coor_x,coor_y] = path[coor_x+1,coor_y] + path[coor_x,coor_y+1] return path path = path_counter(21,21) print(path[1,1])