1/32 the number of (2n+1) X (2n+1) binary arrays with equal numbers of 2 X 2 subblocks with sum mod two being 0 and 1.

A183765

1/32 the number of (2n+1) X (2n+1) binary arrays with equal numbers of 2 X 2 subblocks with sum mod two being 0 and 1.