Hardinian Arrays
Robert Dougherty-Bliss, Manuel Kauers
TL;DR
This paper proves a conjectured recurrence relation for Hardinian arrays, a family of sequences related to king-moves on arrays, and explores their asymptotic behavior.
Contribution
It confirms a conjecture by Kauers and Koutschan and establishes new results on the asymptotics of Hardinian sequences.
Findings
Proved the recurrence conjecture for one Hardinian sequence.
Validated older conjectures from OEIS entries.
Proposed new conjectures on the asymptotic growth of these sequences.
Abstract
In 2014, R.H. Hardin contributed a family of sequences about king-moves on an array to the On-Line Encyclopedia of Integer Sequences (OEIS). The sequences were recently noticed in an automated search of the OEIS by Kauers and Koutschan, who conjectured a recurrence for one of them. We prove their conjecture as well as some older conjectures stated in the OEIS entries. We also have some new conjectures for the asymptotics of Hardin's sequences.
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Taxonomy
TopicsCellular Automata and Applications · semigroups and automata theory