A305027 Array read by antidiagonals: T(n,m) is the number of nonisomorphic binary n X m matrices with 3 1's per column under row and column permutations (m >= 3).

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 4, 7, 5, 1, 1, 1, 4, 11, 17, 6, 1, 1, 1, 4, 14, 40, 35, 9, 1, 1, 1, 4, 15, 62, 122, 76, 11, 1, 1, 1, 4, 16, 78, 272, 410, 149, 15, 1, 1, 1, 4, 16, 87, 427, 1307, 1270, 291, 18, 1, 1, 1, 4, 16, 91, 544, 2754, 6178, 3888, 539, 23, 1

Offset: 0

Author

Andrew Howroyd, May 24 2018

Keywords

• nonn
• tabl

Comments

Also, the number of pure 2-complexes on m nodes with n multiple 2-simplexes.

Examples

			Array begins:
========================================================
n\m| 3  4   5    6     7      8      9     10     11
---+----------------------------------------------------
0  | 1  1   1    1     1      1      1      1      1 ...
1  | 1  1   1    1     1      1      1      1      1 ...
2  | 1  2   3    4     4      4      4      4      4 ...
3  | 1  3   7   11    14     15     16     16     16 ...
4  | 1  5  17   40    62     78     87     91     92 ...
5  | 1  6  35  122   272    427    544    606    635 ...
6  | 1  9  76  410  1307   2754   4251   5343   5939 ...
7  | 1 11 149 1270  6178  18247  36455  54621  67609 ...
8  | 1 15 291 3888 28687 122038 327774 616020 891831 ...
...
		

Links

• StackExchange, How many arrays with crossed cells, order of rows/columns irrelevant, Dec 13 2013

Crossrefs

Columns m=4..7 are A001400, A014395, A050911, A050912.

A diagonal is A247596.

Cf. A050913 (infinite m), A304942.

Programs

PARI

\\ See A304942 for Blocks
for(n=1, 8, for(m=3, 11, print1(Blocks(n, m, 3), ", ")); print)