For any regular cardinal κκ and ordinal η<κ++η<κ++ it is consistent that 2κ2κ is as large as you wish, and every function f:η→[κ,2κ]∩Cardf:η→[κ,2κ]∩Card with f(α)=κf(α)=κ for cf(α)<κcf(α)<κ is the cardinal sequence of some locally compact scattered space.
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