login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A072445 Number of subsets S of the power set P{1,2,...,n} such that: {1}, {2},..., {n} are all elements of S; {1,2,...,n} is an element of S; if X and Y are elements of S and X and Y have a nonempty intersection, then the union of X and Y is an element of S. The sets S are counted modulo permutations on the elements 1,2,...,n. 11
1, 1, 1, 4, 40, 3044, 26894586 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
We define a connectedness system to be a set of finite nonempty sets (edges) that is closed under taking the union of any two overlapping edges. It is connected if it is empty or contains an edge with all the vertices. Then a(n) is the number of unlabeled connected connectedness systems without singletons on n vertices. - Gus Wiseman, Aug 01 2019
LINKS
FORMULA
Inverse Euler transform of A072444. - Andrew Howroyd, Oct 28 2023
EXAMPLE
a(3) = 4 because of the 4 sets: {{1}, {2}, {3}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 2}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 2}, {1, 3}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}.
CROSSREFS
The non-connected case is A072444.
The labeled case is A072447.
The case with singletons is A326869.
Sequence in context: A304985 A292814 A303124 * A000841 A059918 A296101
KEYWORD
nonn,more
AUTHOR
Wim van Dam (vandam(AT)cs.berkeley.edu), Jun 18 2002
EXTENSIONS
a(0)=1 prepended and a(6) corrected by Andrew Howroyd, Oct 28 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)