# Problem 237: Tours on a 4 x n playing board

![graphic](img237.gif)

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?