How many 18-digit number is there such that no digit occurs more than 3 times. All numbers start with a non-zero digit.

digits.py

"""Licensed under GPLv3 <http://www.gnu.org/licenses/>.
Authors:
Santiago Alessandri
Eric Lopes
"""
helpTable = {
    (1, 5) : 5,
    (1, 4) : 6,
    (1, 3) : 7,
    (1, 2) : 8,
    (1, 1) : 9,
    (1, 0) : 10,
}

def s(*v):
    if v in helpTable:
        return helpTable[v]
    if v[0]==1:
        return helpTable[v[:2]]
    result = 0
    cant = 10 - v[1]
    if v[2]:
        result += v[2] * s(v[0] - 1, v[1] + 1, v[2] - 1, v[3])
        cant -= v[2]
    if v[3]:
        result += v[3] * s(v[0] - 1, v[1], v[2] + 1, v[3] - 1)
        cant -= v[3]
    if cant:
        result += cant * s(v[0] - 1, v[1], v[2], v[3] + 1)
    helpTable[v] = result
    return result

if __name__ == '__main__':
    length = 17
    result = 9 * s(length, 0, 0, 1)
    print("The result is:", result)