sympy and lru_cache faster!!

from sympy import sqrt, simplify
from functools import lru_cache

memo = {
        0:2,
        1:(sqrt(6)-sqrt(2))/2
    }

simplify = lru_cache(simplify)

def sinus_seq(n):
    if n in memo:
        return memo[n]
    a1 = sinus_seq(n-1)
    a2 = sinus_seq(n-2)
    memo[n] = simplify((2*(sqrt(6)-sqrt(2))/4)*a1-a2)
    return memo[n]

for i in range(30000):
    print(f"{sinus_seq(i)}")