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Power Partitions and Semi-m-Fibonacci Partitions
Abdulaziz M. Alanazi, Augustine O. Munagi, Darlison Nyirenda
George Andrews recently proved a new identity between the cardinalities of the set of Semi-Fibonacci partitions and the set of partitions into powers of two with all parts appearin…
A simplification and generalization of Elsayed's two-dimensional system of third order difference equations
M. Folly-Gbetoula, D. Nyirenda
A full Lie analysis of a system of third-order difference equations is performed. Explicit solutions, expressed in terms of the initial values, are derived. Furthermore, we give su…
On a system of second-order difference equations
M Folly-Gbetoula, D. Nyirenda
We obtain explicit formulas for the solutions of the system of second-order difference equations of the form $x_{n+ 1} = \frac{x_n y_{n-1}}{y_n (a_n + b_n x_n y_{n - 1})}, \quad y_…
On certain rational recursive sequences of order four
Mensah Folly-Gbetoula, Darlison Nyirenda
We obtain solutions to the recursive sequences of the form where and are arbitrary sequences o…
On certain sixth order difference equations
D. Nyirenda, M. Folly-Gbetoula
We use the Lie group analysis method to investigate the invariance properties and the solutions of \begin{align*} x_{n+1} =\frac{x_{n-5}x_{n-3}}{x_{n-1}(a_n +b_nx_{n-5}x_{n-3})}. \…
The invariance and formulas for solutions of some fifth-order difference equations
D. Nyirenda, M. Folly-Gbetoula
Lie group analysis of the difference equations of the form \begin{align*} x_{n+1} =\frac{x_{n-4}x_{n-3}}{x_{n}(a_n +b_nx_{n-4}x_{n-3}x_{n-2}x_{n-1})}, \end{align*} where and…