4 numbers

main.py

def get_easy_res(n):
    ans = 0
    for a in range(1, n):
        for b in range(1, n):
            for c in range(1, n):
                d = n - a - b - c
                if d <= 0 or a == b or a == c or a == d or b == c or b == d or c == d:
                    continue
                ans += 1
    return ans
	
def get_formula_res(n):
    res = (n - 6) * (n - 5) * (2 * n - 11) // 6
    res += 7 * (n - 6) * (n - 5) // 2
    res += 12 * (n - 6)
    res //= 2

    pair_count = (2 * ((n - 1) // 2) - 6) // 2
    res -= 6 + 3 * pair_count * (3 + 3 + pair_count - 1)
    if (n - 1) % 2 == 1:
        res -= 3 * (n - 2) // 2

    res += ((n - 6) // 3 + 1) * 2

    T = (n - 3) // 2
    ss = T * (n - T - 2)
    if n % 2 == 0:
        ss -= T
    ss -= 2 * ((n - 1) // 3)
    if n % 4 == 0:
        ss += 2
    res -= 3 * ss
    
    if n % 3 == 0:
        res -= 2
    return res

for n in range(10, 150):
    er = get_easy_res(n)
    hr = get_formula_res(n)
    if er != hr:
        print('fail', n, er, hr)