  It is shown that the construction of Yang and Fendley (2004 {\it J. Phys. A:
Math.Gen. {\bf 37}} 8937) to obtainsupersymmetric systems, leads not to the
open XXZ chain with anisotropy $\Delta =-{1/2}$ but to systems having
dimensions given by Jacobstahl sequences.For each system the ground state is
unique. The continuum limit of the spectra of the Jacobstahl systems coincide,
up to degeneracies, with that of the $U_q(sl(2))$ invariant XXZ chain for
$q=\exp(i\pi/3)$. The relation between the Jacobstahl systems and the open XXZ
chain is explained.
