Can We Tile a Checkerboard Obtained by Removing One of the Four Corner Squares of a Standard Checkerboard?

Here is an essential overview about Can We Tile a Checkerboard Obtained by Removing One of the Four Corner Squares of a Standard Checkerboard.

for example, there are 12,988,816 ways to tile a standard 8 by 8 chessboard with dominoes, and the following python script returns 12988816.0.

How many domino tilings are there of the Aztec diamond of order 5?

Abstract. We introduce a family of planar regions, called Aztec diamonds, and study tilings of these regions by dominoes. Our main result is that the Aztec diamond of order n has exactly 2n(n+1)/2 domino tilings.

How many ways are there to cover such a chessboard using dominoes?

For example, there are 12,988,816 ways to tile a standard 8 by 8 chessboard with dominoes, and the following python script returns 12988816.0. For sufficiently large arguments the result will not always round to the correct answer, but for moderate-sized arguments it should. The code looks wrong.