Weighted sums of Lucas numbers of the first and second kind

aBa Mbirika

In the \textit{Fibonacci Quarterly} in 1964, C.~R.~Wall gave the following weighted sum of generalized Fibonacci numbers: ${\sum }_{i=1}^{n}i{G}_i=n{G}_{n+2}-G_{n+3}+G_3$, where $\…