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VMO 2010-Number of coloring a 3.3 square

Source:

December 1, 2010
geometrygeometric transformationrotationsymmetrycombinatorics unsolvedcombinatorics

Problem Statement

Let a positive integer nn.Consider square table 3∗33*3.One use nn colors to color all cell of table such that
each cell is colored by exactly one color.
Two colored table is same if we can receive them from other by a rotation through center of 3∗33*3 table
How many way to color this square table satifies above conditions.
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