A331390 Number of binary matrices with 3 distinct columns and any number of nonzero rows with n ones in every column and rows in nonincreasing lexicographic order.

1, 9, 29, 68, 134, 237, 388, 600, 887, 1265, 1751, 2364, 3124, 4053, 5174, 6512, 8093, 9945, 12097, 14580, 17426, 20669, 24344, 28488, 33139, 38337, 44123, 50540, 57632, 65445, 74026, 83424, 93689, 104873, 117029, 130212, 144478, 159885, 176492, 194360, 213551

Offset: 1

Author

Andrew Howroyd, Jan 15 2020

Keywords

• nonn

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.

Examples

			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]
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Column k=3 of A331126.

Programs

PARI

a(n) = {round(((n+2)/2)^4) - 3*(n+1) + 2}

Formula

a(n) = round(((n+2)/2)^4) - 3*(n+1) + 2.