All Questions

The Domb numbers are given by $$D_n=\sum_{k=0}^n\binom{n}{k}^2\binom{2k}k\binom{2(n-k)}{n-k}\ \ \ (n=0,1,2,\ldots).$$ Such numbers have combinatorial interpretation, see, e.g., http://oeis.org/A002895....

Recall that the Franel numbers are given by $$f_n:=\sum_{k=0}^n \binom{n}{k}^3\ \ \ (n=0,1,\ldots).$$ Question. How to prove my following conjecture? Conjecture. For each odd prime $p$, we have $$\...

Recently (assuming radix-$10$), I showed that, for any $a \in \mathbb{N}_{0}$ that is not a multiple of $10$, there exists a unique value $V(a) \in \mathbb{N}_{0}$ which corresponds to the number of ...