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 by brianjn)
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(N1) + 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.
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Are the same dissection only for N=2.

Posted by Jer
on 20091112 10:07:14 