## Building a tower

### Problem 324

Published on Sunday, 13th February 2011, 10:00 am; Solved by 408; Difficulty rating: 50%Let `f`(`n`) represent the number of ways one can fill a 3×3×`n` tower with blocks of 2×1×1.

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.