yaworsw/euler-manager

---
:id: 405
:name: A rectangular tiling
:url: https://projecteuler.net/problem=405
:content: "We wish to tile a rectangle whose length is twice its width.  \nLet <var>T</var>(0)
  be the tiling consisting of a single rectangle.  \nFor <var>n</var> \\> 0, let <var>T</var>(<var>n</var>)
  be obtained from <var>T</var>(<var>n</var>-1) by replacing all tiles in the following
  manner:\n\n ![p405_tile1.png]({{ images_dir }}/p405_tile1.png)\n\nThe following
  animation demonstrates the tilings <var>T</var>(<var>n</var>) for <var>n</var> from
  0 to 5:\n\n ![p405_tile2.gif]({{ images_dir }}/p405_tile2.gif)\n\nLet <var>f</var>(<var>n</var>)
  be the number of points where four tiles meet in <var>T</var>(<var>n</var>).  \nFor
  example, <var>f</var>(1) = 0, <var>f</var>(4) = 82 and <var>f</var>(10<sup>9</sup>)
  mod 17<sup>7</sup> = 126897180.\n\nFind <var>f</var>(10<sup><var>k</var></sup>)
  for <var>k</var> = 10<sup>18</sup>, give your answer modulo 17<sup>7</sup>.\n\n"