OFFSET
0,7
COMMENTS
A singleton is a part of size 1. An endpoint is a vertex that appears in only one part.
a(n) is also the number of binary matrices with a total of n 1's and every row and column sum at least 2 up to permutation of rows and columns.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
EXAMPLE
The a(8) = 9 matrices are:
[1 1 1 1] [1 1 1] [1 1 1 0] [1 1 1 1]
[1 1 1 1] [1 1 1] [1 1 0 1] [1 1 0 0]
[1 1 0] [0 0 1 1] [0 0 1 1]
.
[1 1] [1 1 0] [1 1 0] [1 1 0 0] [1 1 0 0]
[1 1] [1 1 0] [1 1 0] [1 1 0 0] [1 0 1 0]
[1 1] [1 0 1] [1 0 1] [0 0 1 1] [0 1 0 1]
[1 1] [1 0 1] [0 1 1] [0 0 1 1] [0 0 1 1]
PROG
(PARI) Vec(G(25, 1)) \\ G defined in A369927.
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Feb 06 2024
STATUS
approved