This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A368419 #11 Jan 01 2024 13:30:47 %S A368419 176130,498320,19193670,143035180,348655065 %N A368419 a(n) is the number of reduced stable marriage problem instances of order 5 that generate 16 - n possible stable matchings. %C A368419 "Reduced" instances are counted, as in A351430 for order 4. %C A368419 Reduced instances are fewer than all instances by a factor of n!(n-1)! due to participant-renaming isomorphism, analogous to reduced latin squares. %C A368419 The counts are listed in reverse order from A351430 so that the known terms appear first. The first term gives the number of maximal instances (with 16 stable matchings, per A357269). %C A368419 The total number of reduced instances for order 5 is 214990848000000000, given by A351409(5). %C A368419 The corresponding sequence for order 3 is [91,957,2840], with 91 maximal instances. %C A368419 a(0) = A368433(5) = A344669(5) / (5! * 4!). %C A368419 Results were obtained using the MiniZinc constraint modeling language, by extending the "Model for the Stable Marriage Problem" given in the MiniZinc Handbook, Section 2.2.6. %C A368419 The first two terms were obtained on a PC with 12GB RAM; the next three terms on a PC with 64GB RAM. %D A368419 D. R. Eilers, "The Maximum Number of Stable Matchings in the Stable Marriage Problem of Order 5 is 16". In preparation. %D A368419 Dr Jason Wilson, Director, Biola Quantitative Consulting Center, "Stable Marriage Problem Project Report", crediting team of Annika Miller, Henry Lin, and Joseph Liu; December 22, 2023. %H A368419 A. T. Benjamin, C. Converse, and H. A. Krieger, <a href="https://doi.org/10.1016/0166-218X(95)80006-P">Note. How do I marry thee? Let me count the ways</a>, Discrete Appl. Math. 59 (1995) 285-292. %H A368419 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, [Section 5, Distribution for the number of stable matchings]. %H A368419 D. E. Knuth, <a href="https://www-cs-faculty.stanford.edu/~knuth/ms.html">Mariages Stables</a>, Presses Univ. de Montréal, 1976 (Research Problem #5). %H A368419 David F. Manlove, <a href="https://doi.org/10.1142/8591">Algorithmics of Matching Under Preferences</a>, World Scientific (2013) [Section 2.2.2]. %H A368419 E. G. Thurber, <a href="https://doi.org/10.1016/S0012-365X(01)00194-7">Concerning the maximum number of stable matchings in the stable marriage problem</a>, Discrete Math., 248 (2002), 195-219. %Y A368419 Cf. A351430 (order 4, in reverse order). %Y A368419 Cf. A357269, A351409, A344669, A368433. %K A368419 nonn,more,fini %O A368419 0,1 %A A368419 _Dan Eilers_, Dec 23 2023