Combinatorial Sums $\sum_{k\equiv r(\mbox{mod } m)}{n\choose k}a^k$ and   Lucas Quotients
  In this paper, we study the combinatorial sum $$\sum_{k\equiv r(\mbox{mod }m)}{n\choose k}a^k.$$ By studying this sum, we obtain new congruences for Lucas quotients of two infinite families of Lucas sequences. Only for three Lucas sequences, there are such known results. 
Jiangshuai Yang and Yingpu Deng
math.NT