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%I #13 Feb 11 2022 12:13:21
%S 34080,11484,1092
%N a(n) is the number of preference profiles in the stable marriage problem with 3 men and 3 women that generate n possible stable matchings.
%C A185141(n) is the total number of preference profiles for n men and n women.
%C A185141(3) = 46656 is the sum of the terms of this sequence.
%C For 2 men and 2 women, the total number of preference profiles is 16, where 14 profiles have 1 stable matching, and 2 profiles have 2 stable matchings.
%C For 4 men and 4 women, the total number of preference profiles is 110075314176, where the number of possible stable matchings ranges from 1 to 10, excluding 9. The distribution is provided by sequence A344667(n).
%H Matvey Borodin, Eric Chen, Aidan Duncan, Tanya Khovanova, Boyan Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima Rastogi, and Michael Voigt, <a href="https://arxiv.org/abs/2201.00645">Sequences of the Stable Matching Problem</a>, arXiv:2201.00645 [math.HO], 2021.
%Y Cf. A185141, A344667, A344668, A344669.
%K nonn,bref,fini,full
%O 1,1
%A _Tanya Khovanova_ and MIT PRIMES STEP Senior group, May 27 2021
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