Find an expression which yields the number of ways to split a 2 by N rectangle into two polyominoes. Rotations and reflections are NOT considered distinct.
For example, if N=1 there is only one way - two 1x1 squares.
If N=2 then there are two ways - one way is a 1x1 square with an "L" shape and two 2x1 rectangles as the other.
If N=3 then there are the 6 ways as depicted:
(In reply to Table
I also reached the conclusion that the formula is the triangular numbers, but have been unable to show why. Specifically I have tried to show that there is a recursive pattern F(N) = F(N-1) + N
The reason why N=2 is one number short is easy to see. The 2x2 rectangle is the only square, therefore it has extra symmetry.
++ and #+
Are the same dissection only for N=2.
Posted by Jer
on 2009-11-12 10:07:14