Combinatorial chessboard tilings (Q2883416)

In this paper the number \(a_n\) of ways to tile a \(k\times n\) board using tiles \(T_1,T_2,\ldots ,T_j\) (colored or not) is considered (a tile is placed on the board by transition only). For three examples with \(2\leq j\leq 3\) recurrence and close formulas are deduced. Finally, the AA. assert that the number of ways to tile any \(k\times n\) board \(B\), with \(k\) fixed and using any finite set of tiles, satisfies a linear, homogeneous, constant coefficient recurrence and the same conclusion holds if a finite fixed pattern of squares is deleted from the left (or right) side of \(B\).