Journal of Integer Sequences, Vol. 9 (2006), Article 06.3.6

Periodicity and Parity Theorems for a Statistic on r-Mino Arrangements

Mark A. Shattuck and Carl G. Wagner
Mathematics Department
University of Tennessee
Knoxville, TN 37996-1300
USA

Abstract: We study polynomial generalizations of the r-Fibonacci and r-Lucas sequences which arise in connection with a certain statistic on linear and circular $r$-mino arrangements, respectively. By considering special values of these polynomials, we derive periodicity and parity theorems for this statistic on the respective structures.

(Concerned with sequences A000045 and A000204 .)

Received April 4 2006; revised version received August 17 2006. Published in Journal of Integer Sequences August 18 2006.