A330032 - OEIS

%I #20 Jul 15 2024 09:11:16

%S 1,2,26,9366,204495126,460566381955706,162249649997008147763642,

%T 12595124129900132067036747870669270,

%U 288398561903310939256721956218813835167026180310,2510964964470962082968627390938311899485883615067802615950711482

%N The number of chains of strictly rooted upper triangular or lower triangular matrices of order n.

%C Also, the number of chains in the power set of (n^2-n)/2-elements such that the first term of the chains is either an empty set or a set of (n^2-n)/2-elements.

%C The number of rooted chains of 2-element subsets of {0,1, 2, ..., n} that contain no consecutive integers.

%C The number of distinct rooted reflexive symmetric fuzzy matrices of order n.

%C The number of chains in the set consisting of all n X n reflexive symmetric matrices such that the first term of the chains is either reflexive symmetric 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 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-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

%E Missing term a(6) = 162249649997008147763642 inserted by _Georg Fischer_, Jul 15 2024