cp's OEIS Frontend

A330301 Number of chains of binary reflexive matrices of order n.

%I A330301 #54 Jul 03 2025 04:23:00
%S A330301 1,1,11,18731,112366270379,10710751184977536812459,
%T A330301 45614275176047521934969856784739607851,
%U A330301 19643251901558299817275038399757555422179135786779642874411
%N A330301 Number of chains of binary reflexive matrices of order n.
%C A330301 Also, the number of chains in the power set of (n^2-n) elements.
%C A330301 a(n) is the number of distinct n X n reflexive fuzzy matrices.
%D A330301 S. Nkonkobe and V. Murali, A study of a family of generating functions of Nelsen-Schmidt type and some identities on restricted barred preferential arrangements, Discrete Math., Vol. 340(5) (2017), pp. 1122-1128.
%H A330301 Alois P. Heinz, <a href="/A330301/b330301.txt">Table of n, a(n) for n = 0..21</a>
%H A330301 S. R. Kannan and Rajesh Kumar Mohapatra, <a href="https://arxiv.org/abs/1909.13678">Counting the Number of Non-Equivalent Classes of Fuzzy Matrices Using Combinatorial Techniques</a>, arXiv preprint arXiv:1909.13678 [math.GM], 2019.
%H A330301 V. Murali, <a href="https://doi.org/10.1016/j.fss.2006.03.005">Combinatorics of counting finite fuzzy subsets</a>, Fuzzy Sets Syst., 157(17)(2006), 2403-2411.
%H A330301 V. Murali and B. Makamba, <a href="https://doi.org/10.1080/03081070512331318356">Finite Fuzzy Sets</a>, Int. J. Gen. Syst., Vol. 34 (1) (2005), pp. 61-75.
%H A330301 R. B. Nelsen and H. Schmidt, Jr., <a href="http://www.jstor.org/stable/2690450">Chains in power sets</a>, Math. Mag., 64 (1) (1991), 23-31.
%H A330301 S. Nkonkobe, V. Murali, <a href="http://arxiv.org/abs/1503.06172">A study of a family of generating functions of Nelsen-Schmidt type and some identities on restricted barred preferential arrangements</a>, arXiv:1503.06172 [math.CO] Apr 2015.
%F A330301 a(n) = A007047(n^2-n).
%p A330301 # P are the polynomials defined in A007047.
%p A330301 a := n -> 2^(n^2-n)*subs(x=1/2, P(n^2-n, x)):
%p A330301 seq(a(n), n=0..7);
%t A330301 Array[2 PolyLog[-(#^2-#), 1/2] - 1 &, 8, 0]
%t A330301 Table[2*PolyLog[-(n^2-n), 1/2] - 1, {n, 0, 19}]
%t A330301 Table[LerchPhi[1/2, -(n^2-n), 2]/2, {n, 0, 9}]
%Y A330301 Cf. A007047, A328044.
%K A330301 nonn
%O A330301 0,3
%A A330301 S. R. Kannan, _Rajesh Kumar Mohapatra_, Jan 01 2020