3.py

from itertools import cycle, islice

def coords():
    dirs = cycle([(1,0), (0,1), (-1,0), (0, -1)])
    (dx, dy) = next(dirs)
    yield (0,0)
    minx = miny = maxx = maxy = 0
    x = y = 0
    while True:
        (x,y) = (x + dx, y + dy)
        yield (x,y)
        if x > maxx or x < minx or y > maxy or  y < miny:
            maxx, maxy, minx, miny = (max(x, maxx), max(y,maxy), min(x, minx), min(y, miny))
            (dx, dy) = next(dirs)


def sums():
    board = {(0,0): 1}
    for (x,y) in coords():
        neighbors = (((x+dx), (y+dy)) for dx in xrange(-1,2) for dy in xrange(-1,2))
        val = sum(board.get(n,0) for n in neighbors)
        yield val
        board[(x,y)] = val

target = 277678

#part1
coord = islice(coords(), target, target+1)
print list(abs(x)+abs(y) for (x,y) in coord)[0]

#part2
for x in sums():
    if x > target:
        print x
        break