# Problem 405: A rectangular tiling
We wish to tile a rectangle whose length is twice its width. Let T(0) be
the tiling consisting of a single rectangle. For n > 0, let T(n) be
obtained from T(n-1) by replacing all tiles in the following manner: The
following animation demonstrates the tilings T(n) for n from 0 to 5: Let
f(n) be the number of points where four tiles meet in T(n). For example,
f(1) = 0, f(4) = 82 and f(109) mod 177 = 126897180. Find f(10k) for k =
1018, give your answer modulo 177.