A man and a woman who rank each other last and end up in a marriage are called a hell-couple. A stable matching cannot have more than one hell-couple.
Given a profile, if there exists a stable matching with a hell-couple, then all the stable matchings for this profile have the same hell-couple.
The Gale-Shapley algorithm (both men-proposing and women-proposing) for such a profile needs at least n rounds to terminate.
A344670(n) is the number of preference profiles such that there exists a stable matching with a hell-couple.
This sequence is distinct from A344670 because in this sequence profiles are counted with their respective multiplicity if they yield multiple stable matchings with a hell-couple.