from math import sqrt

def pq(p,q):
	a = -p/2
	b = sqrt(a**2-q)
	return (a+b,a-b)

(l1,l2) = pq(-1,-1)
c2 = -l1/(l2-l1)
c1 = 1-c2

c1 *= l1
c2 *= l2

fib = lambda k: int(c1*pow(l1,k) + c2*pow(l2,k))

if __name__ == '__main__':
	print("fib(k) = (%f) * (%f)^k + (%f) * (%f)^k)" % (c1,l1,c2,l2))

	for i in range(0,51):
		print("%d: %d" %(i,fib(i)))
y