A New Statistic on Linear and Circular $r$-Mino Arrangements - Shattuck, Mark A.; Wagner, Carl G. (The Electronic Journal of Combinatorics, 2006)
We introduce a new statistic on linear and circular $r$-mino arrangements which leads to interesting polynomial generalizations of the $r$-Fibonacci and $r$-Lucas sequences. By studying special values of these polynomials, we derive periodicity and parity theorems for this statistic.