[go: up one dir, main page]

login
A331510
Array read by antidiagonals: A(n,k) is the number of nonequivalent binary matrices with k columns and any number of distinct nonzero rows with n ones in every column up to permutation of rows and columns.
7
1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 3, 1, 0, 1, 1, 5, 4, 0, 0, 1, 1, 7, 12, 3, 0, 0, 1, 1, 11, 36, 23, 1, 0, 0, 1, 1, 15, 124, 191, 30, 0, 0, 0, 1, 1, 22, 412, 2203, 837, 23, 0, 0, 0, 1, 1, 30, 1500, 31313, 41664, 2688, 12, 0, 0, 0, 1
OFFSET
0,8
FORMULA
A(n,k) = 0 for k > 0, n > 2^(k-1).
A(n,k) = A(2^(k-1) - n, k) for k > 0, n <= 2^(k-1).
EXAMPLE
Array begins:
=================================
n\k | 0 1 2 3 4 5 6 7
----+----------------------------
0 | 1 1 1 1 1 1 1 1 ...
1 | 1 1 2 3 5 7 11 15 ...
2 | 1 0 1 4 12 36 124 412 ...
3 | 1 0 0 3 23 191 2203 ...
4 | 1 0 0 1 30 837 ...
5 | 1 0 0 0 23 ...
...
The A(2,3) = 4 matrices are:
[1 1 1] [1 1 0] [1 1 1] [1 1 0]
[1 0 0] [1 0 1] [1 1 0] [1 0 1]
[0 1 0] [0 1 0] [0 0 1] [0 1 1]
[0 0 1] [0 0 1]
CROSSREFS
Rows n=1..3 are A000041, A331717, A331718.
Column k=5 is A331719.
Sequence in context: A339218 A263412 A321258 * A319854 A124035 A204184
KEYWORD
nonn,tabl,more
AUTHOR
Andrew Howroyd, Jan 18 2020
EXTENSIONS
a(58)-a(65) from Andrew Howroyd, Feb 08 2020
STATUS
approved