Counting Fibonacci Squares

Probability Level 1

Consider the above sequence. In step nn, we add Fn F_n (Fibonacci number) unit squares in a column to the right. We want to count the number of squares (of all sizes) in each figure.

If n=1n = 1, then we count 1 square.

If n=2n = 2, then 1 small square is added, so we count 2 1-by-1 squares.

If n=3n = 3, then 2 small squares are added, so we count 4 1-by-1 squares.

If n=4n = 4, then 3 small squares are added, so we count 7 1-by-1 squares and a 2-by-2 square, which altogether makes 8 squares in all.

For n=5n = 5, is the number of all possible different-sized squares 16?

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