Problem 324

Building a tower

Let `f`(`n`) represent the number of ways one can fill a 33`n` tower with blocks of 211.

You're
allowed to rotate the blocks in any way you like; however, rotations,
reflections etc of the tower itself are counted as distinct.

For example (with `q` = 100000007) :`f`(2) = 229,`f`(4) = 117805,`f`(10) mod `q` = 96149360,`f`(10^{3}) mod `q` = 24806056,`f`(10^{6}) mod `q` = 30808124.

Find `f`(10^{10000}) mod 100000007.

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These problems are part of
Project Euler
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