Tiling of dominoes with ranked colors

Abstract Several articles deal with tilings with various colors and shapes. In this paper, we present a new type of tiling problem of a $$(1\times n)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>×</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> —board where the colors have a prescribed order of preference and the size of colored dominoes is bounded by $$(1\times s)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>×</mml:mo> <mml:mi>s</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . 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.