Генерация k наччи чисел

from functools import lru_cache
 
 
@lru_cache
def k_nacci(k, n):
    return 0 if n < k else 1 if n == k else sum(k_nacci(k, n - i) for i in range(1, k + 1))

@lru_cache
def tribonacci(n):
    return 0 if n < 2 else 1 if n == 2 else sum(tribonacci(n - i) for i in range(1, 4))
 
 
@lru_cache
def tetranacci(n):
    return 0 if n < 3 else 1 if n == 3 else sum(tetranacci(n - i) for i in range(1, 5))
 
 
@lru_cache
def pentanacci(n):
    return 0 if n < 4 else 1 if n == 4 else sum(pentanacci(n - i) for i in range(1, 6))
 
 
@lru_cache
def hexanacci(n):
    return 0 if n < 5 else 1 if n == 5 else sum(hexanacci(n - i) for i in range(1, 7))
 
 
@lru_cache
def heptanacci(n):
    return 0 if n < 6 else 1 if n == 6 else sum(heptanacci(n - i) for i in range(1, 8))
 
 
@lru_cache
def octanacci(n):
    return 0 if n < 7 else 1 if n == 7 else sum(octanacci(n - i) for i in range(1, 9))
 
 
@lru_cache
def enneanacci(n):
    return 0 if n < 8 else 1 if n == 8 else sum(enneanacci(n - i) for i in range(1, 10))
 
 
@lru_cache
def decanacci(n):
    return 0 if n < 9 else 1 if n == 9 else sum(decanacci(n - i) for i in range(1, 11))

dp

dp = [ 0 for _ in range(0, n+2)]