Python-сообщество

def partial_sum(seq, start, dir):
    start, stop = (start + 1, len(seq)) if dir > 0 else (0, start)
    return sum(seq[i] for i in xrange(start, stop))
def find_saws(k, n):
    if n < 1:
        return 0
    elif n == 1:
        return k
    else:
        return 2 * sum(reduce(lambda m, v: [partial_sum(m, i, ((v+1)%2)*2-1) for i, _ in enumerate(m)], range(n-2), range(k)))

from itertools import accumulate
def count2(k, n):
    ran = acc = range(1,k+1)
    for l in range(n-1):
        acc = tuple( accumulate(acc[k-p-1] if k>p else 0 for p in ran ) )
    return acc[-1]*2 if n > 1 else k