Some cells of a $2n\times2n$ board are marked so that each cell has an even number of neighboring (i.e. sharing a side) marked cells. Find the number of such markings.
Source: Mongolia MO 2001 Teachers P4
Tags: combinatorics
Some cells of a $2n\times2n$ board are marked so that each cell has an even number of neighboring (i.e. sharing a side) marked cells. Find the number of such markings.