
    Design an algorithm for a social network's friend recommendation system that determines the number of viable connection paths between users, where a path of length n represents increasing interaction strengths, and each subsequent interaction score must be at least double the previous score while not exceeding the platform's maximum interaction score m. The system needs to identify all possible sequences of escalating engagement levels that could form meaningful user connections.
    

    
def get_total_number_of_sequences(m, n):
    """
    Design an algorithm for a social network's friend recommendation system that determines the number of viable connection paths between users, where a path of length n represents increasing interaction strengths, and each subsequent interaction score must be at least double the previous score while not exceeding the platform's maximum interaction score m. The system needs to identify all possible sequences of escalating engagement levels that could form meaningful user connections.
    

    """
def get_total_number_of_sequences(m, n):
    """
    Design an algorithm for a social network's friend recommendation system that determines the number of viable connection paths between users, where a path of length n represents increasing interaction strengths, and each subsequent interaction score must be at least double the previous score while not exceeding the platform's maximum interaction score m. The system needs to identify all possible sequences of escalating engagement levels that could form meaningful user connections.
    

    """
    T = [[0 for i in range(n + 1)] for i in range(m + 1)]
    for i in range(m + 1):
        for j in range(n + 1):
            if i == 0 or j == 0:
                T[i][j] = 0
            elif i < j:
                T[i][j] = 0
            elif j == 1:
                T[i][j] = i
            else:
                T[i][j] = T[i - 1][j] + T[i // 2][j - 1]
    return T[m][n]