Building a tower

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(10³) mod q = 24806056,f(10⁶) mod q = 30808124.

Find f(10¹⁰⁰⁰⁰) mod 100000007.

Written by gamwe6 who lives and works in San Francisco building useful things. You should follow him on Twitter