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

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.

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(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.

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