  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.
