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Apr 10, 2019 at 22:31 comment added Max Alekseyev @SebastianSchlecht: I doubt there is a simple general formula. But for a fixed $n$, it seems to be a polynomial in $l$. For $n=2$ and $n=3$, we have second- and sixth- degree polynomials.
Apr 10, 2019 at 22:26 history edited Max Alekseyev CC BY-SA 4.0
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Apr 10, 2019 at 22:24 comment added Jiro Although, ideally I would prefer a bit more closed Form solution. I had the impression that the generating functions for this problem are rather compact, although I don't know exactly how to get there.
Apr 10, 2019 at 22:16 comment added Jiro that's certainly very helpful! Also I can confirm the solutions to $n=4$.
Apr 10, 2019 at 22:07 history answered Max Alekseyev CC BY-SA 4.0