Abstract

Several researchers have looked at pulsating Fibonacci sequences in the last ten years, which are generalizations of the Fibonacci sequence. They verify the closed form of these sequences via mathematical induction. This approach is beautiful, but it can only be utilized when patterns of the closed forms are predicted. In this paper, we introduce the complex pulsating (a<inf>1</inf>,a<inf>2</inf>,…,a<inf>m</inf>,c)-Fibonacci sequence and apply matrix theory, particularly eigenvalues, eigenvectors, and block matrices, as well as basic properties of the floor function to bridge the gap and obtain the closed form of the complex pulsating. Moreover, the golden ratios of this sequence are provided.