  For any regular cardinal $\kappa$ and ordinal $\eta<\kappa^{++}$ it is
consistent that $2^{\kappa}$ is as large as you wish, and every function
$f:\eta \to [\kappa,2^{\kappa}]\cap Card$ with $f(\alpha)=\kappa$ for
$cf(\alpha)<\kappa$ is the cardinal sequence of some locally compact scattered
space.
