Tours on a 4 x n playing board (noch nicht übersetzt)

Problem 237

Let T(n) be the number of tours over a 4 × n playing board such that:

  • The tour starts in the top left corner.
  • The tour consists of moves that are up, down, left, or right one square.
  • The tour visits each square exactly once.
  • The tour ends in the bottom left corner.

The diagram shows one tour over a 4 × 10 board:

T(10) is 2329. What is T(1012) modulo 108?