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


def assoc_recurrence_memo(base_seq):
    """
    Memo decorator for associated sequences defined by recurrence starting from base

    base_seq(n) -- callable to get base sequence elements

    XXX works only for Pn0 = base_seq(0) cases
    XXX works only for m <= n cases
    """

    cache = []
    def decorator(f):
        def g(n,m):
            L = len(cache)
            if n < L:
                return cache[n][m]

            for i in xrange(L,n+1):
                # get base sequence
                F_i0 = base_seq(i)
                F_i_cache = [F_i0]
                cache.append(F_i_cache)

                # XXX only works for m <= n cases
                # generate assoc sequence
                for j in xrange(1,i+1):
                    F_ij = f(i,j, cache)
                    F_i_cache.append(F_ij)

            return cache[n][m]

        return g
    return decorator