Tangboonduangjit A., Wanasawat S. POWERS OF THE GENERATING MATRIX FOR THE GENERALIZED FIBONACCI SEQUENCE OF ORDER k. ICIC Express Letters Vol.19 No.4 (2025) , 403-410. 410. doi:10.24507/icicel.19.04.403 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/106798
Title
POWERS OF THE GENERATING MATRIX FOR THE GENERALIZED FIBONACCI SEQUENCE OF ORDER k
We establish that under certain conditions, the generating matrix for the generalized Fibonacci sequence of order k can be diagonalized by a Vandermonde matrix. The purpose of this work is to investigate the properties of the generating matrix for the generalized Fibonacci sequence of order k and to derive new results related to its diagonalizability and applications. The results include a closed-form expression for the matrix’s powers and the determinant of a related Toeplitz matrix.
