memoization.py

import functools


def recurrence_memo(initial):
    """
    Memo decorator for sequences defined by recurrence

    See usage examples e.g. in the specfun/combinatorial module
    """
    cache = initial

    def decorator(f):
        @functools.wraps(f)
        def g(n):
            L = len(cache)
            if n <= L - 1:
                return cache[n]
            for i in range(L, n + 1):
                cache.append(f(i, cache))
            return cache[-1]
        return g
    return decorator