def test_find_simple_recurrence():
a = Function('a')
n = Symbol('n')
assert find_simple_recurrence([fibonacci(k) for k in range(12)
]) == (-a(n) - a(n + 1) + a(n + 2))
f = Function('a')
i = Symbol('n')
a = [1, 1, 1]
for k in range(15):
a.append(5 * a[-1] - 3 * a[-2] + 8 * a[-3])
assert find_simple_recurrence(a, A=f, N=i) == (-8 * f(i) + 3 * f(i + 1) -
5 * f(i + 2) + f(i + 3))
assert find_simple_recurrence([0, 2, 15, 74, 12, 3, 0, 1, 2, 85, 4, 5,
63]) == 0
