Lucas numbers are numbers in a sequence defined like this:
```
L(0) = 2
L(1) = 1
L(n) = L(n-1) + L(n-2)
```

Your mission is to complete the function that returns the `n`th term of this sequence.

**Note:** It should work for negative numbers as well; how you do this is you flip the equation around, so for negative numbers: `L(n) = L(n+2) - L(n+1)`


## Examples
```
L(-10) = 123
L(-5)  = -11
L(-1)  =  -1
L(0)   =   2
L(1)   =   1
L(5)   =  11
L(10)  = 123
```

Difficulty: EASY
Starter code: def lucasnum(n):
	

Solutions:
def lucasnum(n):
	a = 2
	b = 1
	flip = n < 0 and n % 2 != 0
	for _ in range(abs(n)):
		(a, b) = (b, a + b)
	return -a if flip else a


SEQUENCE = [2, 1]

def lucasnum(n):
	try:
		return SEQUENCE[abs(n)] * (1, -1)[n < 0 and n % 2]
	except IndexError:
		while len(SEQUENCE) < abs(n) + 1:
			SEQUENCE.append(SEQUENCE[-1] + SEQUENCE[-2])
		return lucasnum(n)


from numpy import matrix

def lucasnum(n):
	return int((matrix('2 1; 1 3') * matrix('0 1; 1 1' if n >= 0 else '-1 1; 1 0', object) ** abs(n))[0, 0])


memo = {0: 2, 1: 1}
current = [-1, 2]

def lucasnum(n):
	while n not in memo:
		if n < 0:
			x = current[0]
			memo[x] = memo[x + 2] - memo[x + 1]
			current[0] -= 1
		else:
			x = current[1]
			memo[x] = memo[x - 2] + memo[x - 1]
			current[1] += 1
	return memo[n]


def lucasnum(n):
	(a, b) = (2, 1)
	for i in range(abs(n)):
		(a, b) = (b, a + b)
	return a * (-1 if n < 0 and n % 2 else 1)


memo = [2, 1]

def lucasnum(n):
	m = abs(n)
	while len(memo) < m + 1:
		memo.append(memo[-1] + memo[-2])
	return memo[m] * (-1) ** (n < 0 and n % 2)


def lucasnum(n):
	(a, b, i) = (2, 1, 0)
	while True:
		if i == n:
			return a
		if n > 0:
			i += 1
			(a, b) = (b, a + b)
		else:
			i -= 1
			(b, a) = (a, b - a)


lucas_sieve = [2, 1, 3, 4, 7]

def lucasnum(n):
	(neg, n) = (1 if n >= 0 or n % 2 == 0 else -1, abs(n))
	return neg * lucas_expand(n)

def lucas_expand(n):
	l = len(lucas_sieve)
	while n >= l:
		lucas_sieve.append(lucas_sieve[l - 1] + lucas_sieve[l - 2])
		l = len(lucas_sieve)
	return lucas_sieve[n]