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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.
2
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
1,2
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
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
Column k=3 of A331126.
Sequence in context: A272784 A272807 A316602 * A273071 A273146 A272844
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 15 2020
STATUS
approved