A. Mbirika

activity

20182025

collaborators

3 papers

math.NT2025

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 $\…

math.NT2021

GCD of sums of $k$ consecutive Fibonacci, Lucas, and generalized Fibonacci numbers

Dan Guyer, aBa Mbirika

We explore the sums of $k$ consecutive terms in the generalized Fibonacci sequence $(G_{n})_{n \geq 0}$ given by the recurrence $G_{n} = G_{n - 1} + G_{n - 2}$ for all $n \geq 2…

math.NT2018

New methods to find patches of invisible integer lattice points

Austin Goodrich, Aba Mbirika, Jasmine Nielsen

It is a surprising fact that the proportion of integer lattice points visible from the origin is exactly $\frac{6}{π ^{2}}$ , or approximately 60 percent. Hence, approximately 40 perce…

Weighted sums of Lucas numbers of the first and second kind

GCD of sums of k consecutive Fibonacci, Lucas, and generalized Fibonacci numbers

New methods to find patches of invisible integer lattice points

GCD of sums of $k$ consecutive Fibonacci, Lucas, and generalized Fibonacci numbers