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

1, 1, 11, 18731, 112366270379, 10710751184977536812459, 45614275176047521934969856784739607851, 19643251901558299817275038399757555422179135786779642874411

Offset: 0

Author

S. R. Kannan, Rajesh Kumar Mohapatra, Jan 01 2020

Keywords

• nonn

Comments

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

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

References

• 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.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..21
• S. R. Kannan and Rajesh Kumar Mohapatra, Counting the Number of Non-Equivalent Classes of Fuzzy Matrices Using Combinatorial Techniques, arXiv preprint arXiv:1909.13678 [math.GM], 2019.
• V. Murali, Combinatorics of counting finite fuzzy subsets, Fuzzy Sets Syst., 157(17)(2006), 2403-2411.
• V. Murali and B. Makamba, Finite Fuzzy Sets, Int. J. Gen. Syst., Vol. 34 (1) (2005), pp. 61-75.
• R. B. Nelsen and H. Schmidt, Jr., Chains in power sets, Math. Mag., 64 (1) (1991), 23-31.
• S. Nkonkobe, V. Murali, A study of a family of generating functions of Nelsen-Schmidt type and some identities on restricted barred preferential arrangements, arXiv:1503.06172 [math.CO] Apr 2015.

Crossrefs

Cf. A007047, A328044.

Programs

Maple

# P are the polynomials defined in A007047.
a := n -> 2^(n^2-n)*subs(x=1/2, P(n^2-n, x)):
seq(a(n), n=0..7);

Mathematica

Array[2 PolyLog[-(#^2-#), 1/2] - 1 &, 8, 0]
Table[2*PolyLog[-(n^2-n), 1/2] - 1, {n, 0, 19}]
Table[LerchPhi[1/2, -(n^2-n), 2]/2, {n, 0, 9}]

Formula

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