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Building a tower

Problem 324

Published on Sunday, 13th February 2011, 10:00 am; Solved by 399

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.