Rectangular Hardinian Arrays

We resolve some open conjectures from the OEIS about Hardinian arrays (see A253217). In particular, we show via the transfer matrix method that H r ( n, k ), the number of n × k Hardinian arrays with parameter r is a polynomial in n of degree r when r and k are fixed and n is sufficiently large. Our implementation of the main result in Maple and Python involves computing with large, sparse matrices, both numeric and symbolic.