Take any square anywhere on the board. It will be part of a 2×2 square. Now only possibilities are
Note that an alternating pattern (RB) ,i.e,
RB is created either in only x axis or only y axis or both.
Hence in first case in every two adjacent columns there will be atleast an
So there is no possibility of two vertical adjacent squares to be of same color. Same kind of argument for case 2
Hence presence of just one unidirectional would create a y-axis or x-axis alternating pattern.
So, in each case we just need to decide what colour to start with( I mean the squares of first row or column) and there must be at least one repeatition so that only in one direction alternating pattern occurs.
So, 2^8 -2 for x axis
2^8 -2 for y axis
And 2 for all 2×2 squares to be bidirectional,i.e, no unidirectional square or repeatition of colours.