# Is there a formula for the number of ways an $N\times N$ grid can be filled with squares?

How many ways are there to fill an $n\times n$ board with squares with varying sizes?

• you want it completely filled right? – Jorge Fernández Hidalgo Jul 31 '16 at 5:57
• the board, that is .... – Jorge Fernández Hidalgo Jul 31 '16 at 5:57
• Interesting problem, did you have any preliminary thoughts or results? – Joffan Jul 31 '16 at 5:57
• Yes, meaning, there are no rectangular shapes left. – SoloNasus Jul 31 '16 at 5:58
• oeis.org/A045846 – Marcus Andrews Jul 31 '16 at 6:31