Перебор с суммированием?

import numpy as np
 
ls = np.array((256, 304, 397, 465, 477, 497))
val = 4600
 
def main():
    k = np.zeros_like(ls)
    
    def check(i=0):
        v = sum(ls * k)
        if v == val:
            raise ValueError(k)
        elif v > val:
            k[i] = 0
            k[i + 1] += 1
            check(i + 1)        
    
    while True:
        k[0] += 1
        print(k)
        check()
 
main()

n = 5
dp = [''] * (n + 1)
dp[0] = '0'
for step in 2, 3:
    for i in range(n - step, -1, -1):
        if dp[i]:
            for j in range(i + step, n + 1, step):
                if not dp[j]:
                    dp[j] = f'{dp[i]}+{step}*{(j - i) // step}'
    print(dp)
print(dp[-1][2:] if dp[-1] else 'извини, не смогда')