OFFSET
1,2
COMMENTS
The condition that the rows be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of rows.
a(n) is the number of T_0 n-regular set multipartitions (multisets of sets) on a 3-set.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = round(((n+2)/2)^4) - 3*(n+1) + 2.
EXAMPLE
The a(2) = 9 matrices are:
[1, 0, 0] [1, 1, 0] [1, 0, 1] [1, 0, 0]
[1, 0, 0] [1, 0, 0] [1, 0, 0] [1, 0, 0]
[0, 1, 0] [0, 1, 0] [0, 1, 0] [0, 1, 1]
[0, 1, 0] [0, 0, 1] [0, 1, 0] [0, 1, 0]
[0, 0, 1] [0, 0, 1] [0, 0, 1] [0, 0, 1]
[0, 0, 1]
.
[1, 1, 1] [1, 1, 0] [1, 1, 0] [1, 0, 1] [1, 1, 0]
[1, 0, 0] [1, 0, 1] [1, 0, 0] [1, 0, 0] [1, 0, 1]
[0, 1, 0] [0, 1, 0] [0, 1, 1] [0, 1, 1] [0, 1, 1]
[0, 0, 1] [0, 0, 1] [0, 0, 1] [0, 1, 0]
PROG
(PARI) a(n) = {round(((n+2)/2)^4) - 3*(n+1) + 2}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 15 2020
STATUS
approved