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In this post, we consider the same problem as in the previous post but for grids of odd size. As much of the setup was discussed in th...

For $m<n$, it is easy to show that, $\displaystyle\frac{x^m}{(x-a_0)(x-a_1)\cdots(x-a_{n-1})}=\sum_{k=0}^{n-1}\frac{a_k^m}{x-a_k}\...

Ever since I first encountered Polya's Enumeration theorem (PET) to solve a problem from Project Euler, it has continued to fascina...

I recently found a nice identity about Partial fractions on Interesting identities about Partial fractions . The same could also be fou...

Let's say we are given a sequence of $2n$ terms and were told that these are generated by a linear recurrence of order $n$ with the...

This post is inspired by the A collection of grid counting problems . The entire wordpress page is a great read and I thoroughly enjoy ...

Euler's theorem in Geometry is a great result that connects the distance between the circumcentre and incentre of a triangle with ...