Exact Determinants of the RFPrLrR Circulant Involving Jacobsthal, Jacobsthal-Lucas, Perrin and Padovan Numbers

Circulant matrix family occurs in various fields, applied in image processing, communications, signal processing, encoding and preconditioner. Meanwhile, the circulant matrices [1, 2] have been extended in many directions recently. The f(x)-circulant matrix is another natural extension of the research category, please refer to [3, 11]. Recently, some authors researched the circulant type matrices with famous numbers. In [3], Shen et al. discussed the explicit determinants of the RFMLR and RLMFL circulant matrices involving certain famous numbers. Jaiswal [4] showed some determinants of circulant matrices whose elements are the generalized Fibonacci numbers. Lind presented the determinants of circulant and skew circulant involving Fibonacci numbers in [5]. Gao et al. [6] considered the determinants and inverses of skew circulant and skew left circulant matrices with Fibonacci and Lucas numbers. Akbulak and Bozkurt [7] proposed some properties of Toeplitz matrices involving Fibonacci and Lucas numbers. In [8], authors considered circulant matrices with Fibonacci and Lucas numbers and proposed their explicit determinants and inverses by constructing the transformation matrices. Jiang and Hong gave exact determinants of some special circulant matrices involving four kinds of famous numbers in [9]. See more of the literatures in [10, 11, 12]. We introduce two new patten matrices, i.e. row