def luhn_validation(credit_card_number: str) -> bool:
    """
    Function to luhn algorithm validation for a given credit card number.
    >>> luhn_validation('4111111111111111')
    True
    >>> luhn_validation('36111111111111')
    True
    >>> luhn_validation('41111111111111')
    False
    """
    cc_number = credit_card_number
    total = 0
    half_len = len(cc_number) - 2
    for i in range(half_len, -1, -2):
        #  double the value of every second digit
        digit = int(cc_number[i])
        digit *= 2
        # If doubling of a number results in a two digit number
        # i.e greater than 9(e.g., 6 × 2 = 12),
        # then add the digits of the product (e.g., 12: 1 + 2 = 3, 15: 1 + 5 = 6),
        # to get a single digit number.
        if digit > 9:
            digit %= 10
            digit += 1
        cc_number = cc_number[:i] + str(digit) + cc_number[i + 1 :]
        total += digit

    # Sum up the remaining digits
    for i in range(len(cc_number) - 1, -1, -2):
        total += int(cc_number[i])

    return total % 10 == 0