  Recently Kauers, Koutschan and Spahn announced a significant increase in the
length of the so-called {\em gerrymander sequence}, given as A348456 in the
OEIS, extending the sequence from 3 terms to 7 terms. We give a further
extension to 11 terms, but more significantly prove that the coefficients grow
as $\lambda^{4L^2},$ where $\lambda \approx 1.7445498, $ and is equal to the
corresponding quantity for self-avoiding walks crossing a square (WCAS), or
self-avoiding polygons crossing a square (PCAS). These are, respectively, OEIS
sequences A007764 and A333323. Thus we have established a close connection
between these previously separate problems.
  We have also related the sub-dominant behaviour to that of WCAS and PCAS,
allowing us to conjecture that the coefficients of the gerrymander sequence
A348456 grow as $\lambda^{4L^2+dL+e} \cdot L^g,$ where $d=-8.08708 \pm 0.0002,$
$e \approx 7.69$ and $g = 0.75 \pm 0.01,$ with $g$ almost certainly $3/4$
exactly.
  We also have generated 26 terms in the related gerrymander polynomial
(defined below), and have been able to predict the asymptotic behaviour with a
satisfying degree of precision. Indeed, it behaves exactly as $L$ times the
corresponding coefficient of the generalised gerrymander sequence.
  The improved algorithm we give for counting these sequences is a variation of
that which we recently developed for extending a number of sequences for SAWs
and SAPs crossing a domain of the square or hexagonal lattices. It makes use of
a minimal perfect hash function and in-place memory updating of the arrays for
the counts of the number of paths.
