data/problems/324.yml
---
:id: 324
:name: Building a tower
:url: https://projecteuler.net/problem=324
:content: "Let <var>f</var>(<var>n</var>) represent the number of ways one can fill
a 3×3×<var>n</var> tower with blocks of 2×1×1. \nYou're allowed to rotate the
blocks in any way you like; however, rotations, reflections etc of the tower itself
are counted as distinct.\n\nFor example (with <var>q</var> = 100000007) : \n<var>f</var>(2)
= 229, \n<var>f</var>(4) = 117805, \n<var>f</var>(10) mod <var>q</var> = 96149360,
\ \n<var>f</var>(10<sup>3</sup>) mod <var>q</var> = 24806056, \n<var>f</var>(10<sup>6</sup>)
mod <var>q</var> = 30808124.\n\nFind <var>f</var>(10<sup>10000</sup>) mod 100000007.\n\n"