Tiling of dominoes with ranked colors

Several articles deal with tilings with various colors and shapes. In this paper, we present a new type of tiling problem of a \((1\times n)\) $(1\times n)$ —board where the colors have a prescribed order of preference and the size of colored dominoes is bounded by \((1\times s)\) $(1\times s)$ . We show that the total number of tilings can be given as a linearly recurrent sequence of order ks, and at the same time by a higher order self-convolution of s-generalized Fibonacci sequences.