A330032 The number of chains of strictly rooted upper triangular or lower triangular matrices of order n.

1, 2, 26, 9366, 204495126, 460566381955706, 162249649997008147763642, 12595124129900132067036747870669270, 288398561903310939256721956218813835167026180310, 2510964964470962082968627390938311899485883615067802615950711482

Offset: 0

Author

S. R. Kannan, Rajesh Kumar Mohapatra, Feb 29 2020

Keywords

• nonn

Comments

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.

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

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

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.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..28
• 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.
• R. B. Nelsen and H. Schmidt, Jr., Chains in power sets, Math. Mag., 64 (1) (1991), 23-31.
• M. Tărnăuceanu, The number of chains of subgroups of a finite elementary abelian p-group, arXiv preprint arXiv:1506.08298 [math.GR], 2015.

Crossrefs

Cf. A000629, A038719, A007047, A328044, A330301, A330302, A330804, A331957.

Formula

a(n) = A000629((n^2-n)/2).

Extensions

Missing term a(6) = 162249649997008147763642 inserted by Georg Fischer, Jul 15 2024