Counting Block Combinations I
Problem Statement
A row measuring seven units in length has red blocks with a minimum length of three units placed on it, such that any two red blocks (which are allowed to be different lengths) are separated by at least one grey square. There are exactly seventeen ways of doing this.
How many ways can a row measuring $10^{9 \times 2^N}$ units in length be filled? Give your answer modulo $1000000007$.
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You need to submit in the format: "N:problem(N)", possibly with multiple values at once, separated by commas, with $N$ between $1$ and $100$.
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