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!)
A054976 Number of binary n X n matrices with no zero rows or columns, up to row and column permutation. 19
1, 3, 17, 179, 3835, 200082, 29610804, 13702979132, 20677458750966, 103609939177198046, 1745061194503344181714, 99860890306900024150675406, 19611238933283757244479826044874, 13340750149227624084760722122669739026, 31706433098827528779057124372265863803044450 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Also the number of non-isomorphic set multipartitions (multisets of sets) with n parts and n vertices. - Gus Wiseman, Nov 18 2018
LINKS
FORMULA
a(n) = A002724(n) - 2*A002725(n-1) + A002724(n-1).
EXAMPLE
From Gus Wiseman, Nov 18 2018: (Start)
Inequivalent representatives of the a(3) = 17 matrices:
100 100 100 100 100 010 010 001 001 001 001 110 101 101 011 011 111
100 010 001 011 011 001 101 001 101 011 111 101 011 011 011 111 111
011 001 011 011 111 111 011 111 011 111 111 011 011 111 111 111 111
Non-isomorphic representatives of the a(1) = 1 through a(3) = 17 set multipartitions:
{{1}} {{1},{2}} {{1},{2},{3}}
{{2},{1,2}} {{1},{1},{2,3}}
{{1,2},{1,2}} {{1},{3},{2,3}}
{{1},{2,3},{2,3}}
{{2},{1,3},{2,3}}
{{2},{3},{1,2,3}}
{{3},{1,3},{2,3}}
{{3},{3},{1,2,3}}
{{1,2},{1,3},{2,3}}
{{1},{2,3},{1,2,3}}
{{1,3},{2,3},{2,3}}
{{3},{2,3},{1,2,3}}
{{1,3},{2,3},{1,2,3}}
{{2,3},{2,3},{1,2,3}}
{{3},{1,2,3},{1,2,3}}
{{2,3},{1,2,3},{1,2,3}}
{{1,2,3},{1,2,3},{1,2,3}}
(End)
MATHEMATICA
A002724 = Cases[Import["https://oeis.org/A002724/b002724.txt", "Table"], {_, _}][[All, 2]];
A002725 = Cases[Import["https://oeis.org/A002725/b002725.txt", "Table"], {_, _}][[All, 2]];
a[n_] := A002724[[n + 1]] - 2 A002725[[n]] + A002724[[n]];
a /@ Range[1, 13] (* Jean-François Alcover, Sep 14 2019 *)
CROSSREFS
Column sums of A057150.
Sequence in context: A053934 A159592 A126443 * A304863 A163886 A340881
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, May 27 2000
EXTENSIONS
More terms from David Wasserman, Mar 06 2002
Terms a(14) and beyond from Andrew Howroyd, Apr 11 2020
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 19 01:34 EDT 2024. Contains 370952 sequences. (Running on oeis4.)