Journal of Integer Sequences, Vol. 18 (2015), Article 15.7.8

An Integer Sequence Motivated by Generalized Quadrangles

Brian G. Kronenthal
Department of Mathematics
Kutztown University of Pennsylvania
15200 Kutztown Road
Kutztown, PA 19530-9335


In this paper, we prove a closed form for a sequence motivated by the search for new generalized quadrangles of odd order. We present two proofs: a direct proof to explain the closed form’s derivation and a shorter inductive argument. The sequence in question is derived from congruences that arise from applying the Hermite-Dickson criterion to a permutation polynomial that is related to the girth of monomial graphs.

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(Concerned with sequences A246800 A247984.)

Received February 10 2015; revised versions received July 10 2015. Published in Journal of Integer Sequences, July 16 2015.

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