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How to write this function in a nicer way?

Hi all,

Here is a counting formula that has been derived using some recursion formulas but I think it should have a much more elegant form. Any help writing it in " a nicer form " would be really appreciated.

Here is the formula :

\[ P(n, m) = \lfloor \dfrac{m}{2} \rfloor (2 \lfloor \dfrac{n}{3} \rfloor + \dddot{n} ) + \ddot{m} { \{ \dfrac{n}{3} } \} \]


  • \( \dddot{n} \) is the the remainder of n mod 3,

  • \( \ddot{m} \) is the the remainder of m mod 2,

  • \( \{ k \} \) is the integer part of the rational number k.

I expect this function (if derived correctly) is symmetric s.t. P(n,m) = P(m,n) but its no obvious in this current form.

Thanks and enjoy...

EDIT : I found a mistake in the derivation, please ignore :)

Note by Roberto Nicolaides
10 months ago

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