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%I #17 Mar 15 2020 09:45:32
%S 1,2,150,14174522,10631309363962710,213394730876951551651166996282,
%T 288398561903310939256721956218813835167026180310,
%U 55313586130829865212025793302979452922870356482030868613037427298852922
%N The number of rooted chains in the lattice of (0, 1) matrices of order n.
%C Also, the number of n X n distinct rooted fuzzy matrices.
%C The number of chains in the power set of n^2-elements such that the first term of the chains is either an empty set or a set of n^2-elements.
%C The number of chains in the collection of all binary (crisp or Boolean or logical) matrices of order n such that the first term of the chains is either null matrix or unit matrix.
%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 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 M. Tărnăuceanu, <a href="http://www.jstor.org/stable/2690450">The number of chains of subgroups of a finite elementary abelian p-group</a>, arXiv preprint arXiv:1506.08298 [math.GR], 2015.
%F a(n) = A000629(n^2).
%Y Cf. A000629, A038719, A007047, A328044, A330301, A330302, A330804, A331957.
%K nonn
%O 0,2
%A S. R. Kannan, _Rajesh Kumar Mohapatra_, Feb 29 2020
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