On some gaussian oresme numbers

Abstract

Sequences with recurrence relations are used in many branches of science such as mathematics, physics and engineering. The most well-known and studied sequence among these is Horadam sequence. This sequence is a generalization of many sequences and has an important place in the literature. New sequences can also be obtained from this sequence by changing the initial conditions. The most common sequences obtained by this method in the literature are Fibonacci sequence, Lucas sequence and Jacobstal sequence. The Fibonacci sequence, which has an important place among these sequences, has been studied by many authors. Horadam, who also worked on Fibonacci sequences, defined these sequences in complex space and discussed Gaussian Fibonacci sequences. A new sequence, which was defined by Nicole Oresme in the fourteenth century and called the Oresme sequence, is a special case of the Horadam sequence whose initial conditions are rational numbers. Subsequently, this was reviewed by many authors. Based on these studies, Gaussian Oresme number sequences were studied. In this study, we obtained some identities of Gaussian Oresme sequences. We have obtained some sum formulas of Gaussian Oresme numbers. We obtained the matrix for the Gaussian Oresme sequences and calculated the nth power. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.