If we have an n amount of building blocks, and we are tasked with making, what I have found out are 'Young Tableau' like structures (though I am unsure if they are exactly the same), how many can we make out of the n amount of blocks. The trick is that for every two consecutive columns the next one is at most as high as the previous one (i is at least as high as i + 1.) and the same applies to rows. So for example 3 blocks can be built like this:
1
2 1
3 2 3 1 2 3
So out of 3 blocks, we can make 3 structures following these rules. Then 5 out of 4 blocks, 7 out of 5, 10 out of 6. My problem is that I am unable to generalize this into a working equation, so for example how many structures we can make out of 15 blocks, is absolutely beyond me. Any help is appreciated