A strait-forward implementation for the problem: http://www.careercup.com/question?id=14968041

coil.py

# Problem description: http://www.careercup.com/question?id=14968041
def find_coil(n, x, y, dxs, dys):
    nsteps = []
    for nstep in xrange(2, n - 1, 2):
        nsteps.append(nstep)
        nsteps.append(nstep)
    nsteps.append(nstep + 1)

    rs = [y * n + x + 1]
    idx = 0
    for nstep in nsteps:
        for _ in xrange(nstep):
            x += dxs[idx]
            y += dys[idx]
            rs.append(y * n + x + 1)
        idx = (idx + 1) % len(dxs)

    return rs

def coil(n):
    # find coils
    print find_coil(4 * n, 2 * n - 1, 2 * n, [0, 1, 0, -1], [-1, 0, 1, 0])
    print find_coil(4 * n, 2 * n, 2 * n - 1, [0, -1, 0, 1], [1, 0, -1, 0])

coil(2)