Now this makes sense because the x values change based on the column being even or odd

a prime number appears once (2^(1-1)) in a column.

a product of two primes appears twice (2^(2-1)) in a column.

a product of three primes appears four (2^(3-1)) times in a column.

a product of four primes appears eight (2^(4-1)) times in a column.

a product of five primes appears sixteen (2^(5-1)) times in a column.

focus on solving it for odd x+n and it will expand into all 4 solutions.