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A330032 The number of chains of strictly rooted upper triangular or lower triangular matrices of order n. 0
1, 2, 26, 9366, 204495126, 460566381955706, 12595124129900132067036747870669270, 288398561903310939256721956218813835167026180310, 2510964964470962082968627390938311899485883615067802615950711482 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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
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.
FORMULA
a(n) = A000629((n^2-n)/2).
CROSSREFS
Sequence in context: A318132 A134795 A268667 * A273381 A094680 A259326
KEYWORD
nonn
AUTHOR
S. R. Kannan, Rajesh Kumar Mohapatra, Feb 29 2020
STATUS
approved

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Last modified April 16 19:21 EDT 2024. Contains 371754 sequences. (Running on oeis4.)