How to calculate the different combinations of an N×M grid with 3-valid values

Question

I have 3 valid values: a,b,c I can insert them in a N×3 grid in such a way that no row or column contains cells that are the same values. How can I calculate the number of valid patterns that can be created using N rows?

For example, if N = 4, the total number of valid pattern is 296490.

This is my attempt:

def countPatterns(n):

    dp1, dp2 = 6,6
    mod = 10 ** 9 + 7
    
    for i in range(2, n+1):
        dp1, dp2 = (dp1 * 3 + dp2 * 2) % mod, (dp1 * 2 + dp2 * 2) % mod
    return (dp1 + dp2) % mod

When N = 4, the output should be 174 but I'm getting 54.