There is an equilateral triangle consist of 3 mirrors. There is a tiny slit in the corners of the triangle, which can let a laser beam pass through.
We label the 3 slits as A, B and C. There only exists two ways (see the picture above) make a laser beam enter our triangle though C, reflects 11 times in ther triangle, and exit from the triangle though C. The 2 ways are symmetry.
Here is the question for you, our great programmer. How many ways we can make a laser beam enter the triangle though C and exit though C, and the beam reflects n times in the triangle? e.g. there are 80840 ways when n is 1000001.