
    Given a patient's medication regimen of n sequential prescriptions and a maximum safe dosage multiplier m, determine the number of possible safe prescription combinations where each subsequent medication's relative potency must be at least twice but no more than m times the previous medication's potency. The function should consider all possible valid sequences that maintain these safety thresholds between consecutive medications while ensuring no medication exceeds the maximum allowable potency ratio m.
    

    
def get_total_number_of_sequences(m, n):
    """
    Given a patient's medication regimen of n sequential prescriptions and a maximum safe dosage multiplier m, determine the number of possible safe prescription combinations where each subsequent medication's relative potency must be at least twice but no more than m times the previous medication's potency. The function should consider all possible valid sequences that maintain these safety thresholds between consecutive medications while ensuring no medication exceeds the maximum allowable potency ratio m.
    

    """
def get_total_number_of_sequences(m, n):
    """
    Given a patient's medication regimen of n sequential prescriptions and a maximum safe dosage multiplier m, determine the number of possible safe prescription combinations where each subsequent medication's relative potency must be at least twice but no more than m times the previous medication's potency. The function should consider all possible valid sequences that maintain these safety thresholds between consecutive medications while ensuring no medication exceeds the maximum allowable potency ratio m.
    

    """
    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]