
    Design an algorithm to determine the number of possible learning progression paths where a student must achieve n sequential milestones, with each milestone requiring at least double the proficiency level of the previous one, and no milestone can exceed the maximum achievable score m. Each proficiency level must be a positive integer, representing measurable skill benchmarks in the subject.
    

    
def get_total_number_of_sequences(m, n):
    """
    Design an algorithm to determine the number of possible learning progression paths where a student must achieve n sequential milestones, with each milestone requiring at least double the proficiency level of the previous one, and no milestone can exceed the maximum achievable score m. Each proficiency level must be a positive integer, representing measurable skill benchmarks in the subject.
    

    """
def get_total_number_of_sequences(m, n):
    """
    Design an algorithm to determine the number of possible learning progression paths where a student must achieve n sequential milestones, with each milestone requiring at least double the proficiency level of the previous one, and no milestone can exceed the maximum achievable score m. Each proficiency level must be a positive integer, representing measurable skill benchmarks in the subject.
    

    """
    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]