A330301 - OEIS

%I #50 Jan 21 2020 13:43:31

%S 1,1,11,18731,112366270379,10710751184977536812459,

%T 45614275176047521934969856784739607851,

%U 19643251901558299817275038399757555422179135786779642874411

%N Number of chains of binary reflexive matrices of order n.

%C Also, the number of chains in the power set of (n^2-n) elements.

%C a(n) is the number of distinct n X n reflexive fuzzy matrices.

%D 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 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 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 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 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 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 a(n) = A007047(n^2-n).

%p # P are the polynomials defined in A007047.

%p a := n -> 2^(n^2-n)*subs(x=1/2, P(n^2-n, x)):

%p seq(a(n), n=0..7)

%t Array[2 PolyLog[-(#^2-#), 1/2] - 1 &, 8, 0]

%t Table[2*PolyLog[-(n^2-n), 1/2] - 1, {n, 0, 19}]

%t Table[LerchPhi[1/2, -(n^2-n), 2]/2, {n, 0, 9}]

%Y Cf. A007047, A328044.

%K nonn

%O 0,3

%A S. R. Kannan, _Rajesh Kumar Mohapatra_, Jan 01 2020