project-euler/164_numbers_consecutive_digits.py

#!/usr/bin/env python3

cache = [[{0 : 1} for b in range(10)] for a in range(10)]

def f(i, a=0, b=0, fst=1):
    if i in cache[a][b]:
        return cache[a][b][i]
    r = sum((f(i-1, b, n, 0) for n in range(fst, 10-a-b)))
    cache[a][b][i] = r
    return r

print(f(20))