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bw in nxn chessboard so that in every 2x2 both colors have same number

Source: 11th QEDMO p4 Juniors (6-8. 12. 2012) https://artofproblemsolving.com/community/c1512515_qedmo_200507

May 16, 2021
combinatoricsChessboardColoring

Problem Statement

The fields of an n×nn\times n chess board are colored black and white, such that in every small 2×22\times 2-square both colors should be the same number. How many there possibilities are for this?
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