# A Piece of P.I.E

A $$4 \times 4$$ square is made up of 16 $$1 \times 1$$ squares, each of which is coloured either black or white. Let $$n$$ be the number of these $$4 \times 4$$ squares such that within the $$4 \times 4$$ square there are no $$3 \times 3$$ squares made up entirely of white $$1 \times 1$$ squares. What is the digit sum of $$n?$$

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