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The Fibonacci Numbers consist of the sequence of integers: F₀ = 0, F₁ = 1, F₂ = 1, F₃ = 2, F₄ = 3, F₅ = 5, F₆ = 8, F₇ = 13, F₈ = 21, F₉ = 34, F₁₀ = 55, ... . These are defined recursively by the following formula:

What I'm calling the "matrix formula for Fibonacci Numbers" is the following, that we proved by induction:

The next sequence of formulas comes from squaring the above, and using the above formula with "n" replaced by "2n".

Now just take the first equal to the last above:

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