Combinatorial Sums $\sum_{k\equiv r(\mbox{mod} m)}{n\choose k}a^k$ and   Lucas Quotients (II)
  In [16], we obtained some congruences for Lucas quotients of two infinite families of Lucas sequences by studying the combinatorial sum $$\sum_{k\equiv r(\mbox{mod}m)}{n\choose k}a^k.$$ In this paper, we show that the sum can be expressed in terms of some recurrent sequences with orders not exceeding $\varphi{(m)}$ and give some new congruences. 
Jiangshuai Yang and Yingpu Deng
math.NT