cp's OEIS Frontend

A371810 a(n) is the number of pseudo-Latin stable matchings in a particular matrix of size n (see Comments for detail).

%I A371810 #15 May 17 2025 19:22:52
%S A371810 1,2,3,10,12,32,54,268,288,656,1044,4360,5472,15632,26424,195472,
%T A371810 200832,423104,650736,2404960,2950272,8146112,13758624,85524160,
%U A371810 93450240
%N A371810 a(n) is the number of pseudo-Latin stable matchings in a particular matrix of size n (see Comments for detail).
%C A371810 This sequence arose from an attempt to reproduce A069124 by following the description in Thurber, 2002.
%C A371810 Define a matrix G for powers of 2, by G(1)=[1], and G(2^(k+1)) of size 2^(k+1) X 2^(k+1) by the block matrix [G(2^k), G(2^k)+2^k; G(2^k)+2^k, G(2^k)], where G(2^k)+2^k means add 2^k to each element of G(2^k) [see Thurber, p. 198 for more detail].
%C A371810 This sequence computes the number of pseudo-Latin stable matchings in the upper left n X n submatrix of G. Again, consult Thurber for definitions of what constitutes a stable matching in this situation.
%C A371810 Thurber's computation of these values are presented in A069124, but an attempt to reproduce that sequence gave the numbers of this sequence. The values here appear to be always increasing (unlike A069124). This is interesting because much of the Thurber paper is concerned with proving that the number of pseudo-Latin stable matchings is strictly increasing.
%C A371810 The first point of difference with A069124 occurs at n=7, but note that some later values do agree.
%C A371810 Subsequent verification by Dan Eilers in A069194 indicates that it is likely this sequence which is incorrect. - _Sean A. Irvine_, May 17 2025
%H A371810 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a371/A371810.java">Java program</a> (github)
%H A371810 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 A371810 Cf. A069124.
%K A371810 nonn,more
%O A371810 1,2
%A A371810 _Sean A. Irvine_, Apr 06 2024