The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A002416

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A002416

a(n) = 2^(n^2).
(history; published version)

#107 by Michel Marcus at Thu Dec 29 06:03:09 EST 2022

STATUS

reviewed

approved

#106 by Kevin Ryde at Thu Dec 29 01:16:48 EST 2022

STATUS

proposed

reviewed

#105 by Kevin Ryde at Thu Dec 29 01:16:35 EST 2022

STATUS

editing

proposed

#104 by Kevin Ryde at Thu Dec 29 01:14:44 EST 2022

COMMENTS

For n >= 1 , a(n) is the number of n X n (0, 1) matrices.

Also number of distinct square binary images of side length n. - Tyler Busby, Dec 28 2022

STATUS

proposed

editing

Discussion

Thu Dec 29

01:16

Kevin Ryde: Drop comment as same as existing.  A binary image is an 0,1 matrix.  Both are pretty easy things.

#103 by Michel Marcus at Wed Dec 28 13:50:17 EST 2022

STATUS

editing

proposed

Discussion

Wed Dec 28

18:31

Kevin Ryde: When you say existing comment is similar, you mean identical ?!

20:15

Tyler Busby: They are different names for the same underlying structure, but the comment is not identical. I will not be upset if the comment does not get published, but I thought it was worth suggesting as it approaches the sequence from a different field of study.

#102 by Michel Marcus at Wed Dec 28 13:50:09 EST 2022

LINKS

S. R. Kannan, and Rajesh Kumar Mohapatra, <a href="https://arxiv.org/abs/1909.13678">Counting the Number of Non-Equivalent Classes of Fuzzy Matrices Using Combinatorial Techniques</a>, arXiv:1909.13678 [math.GM], 2019.

FORMULA

a(n) = 2^n * Sum_{i = 0...C(n, 2)} C(C(n, 2), i)*3^i. The summation conditions on i, 0 <= i <= C(n, 2), the number of 1's above the main diagonal in the matrix representations of the relations on {1, 2, ..., n}. - Geoffrey Critzer, Feb 18 2011

STATUS

proposed

editing

#101 by Tyler Busby at Wed Dec 28 13:39:13 EST 2022

STATUS

editing

proposed

#100 by Tyler Busby at Wed Dec 28 13:33:53 EST 2022

COMMENTS

Also number of distinct square binary images of side length n. _- _Tyler Busby_, Dec 28 2022

Discussion

Wed Dec 28

13:39

Tyler Busby: Somewhat of a similar comment to the first, because "n X n (0, 1) matrices" and "square binary images of side length n" are at some level the same. But I believe the distinction is interesting enough to be noted.

#99 by Tyler Busby at Wed Dec 28 13:33:35 EST 2022

COMMENTS

Also number of distinct square binary images of side length n. Tyler Busby, Dec 28 2022

STATUS

approved

editing

#98 by Charles R Greathouse IV at Thu Sep 08 08:44:30 EDT 2022

PROG

(MAGMAMagma) [2^(n^2): n in [0..15]]; // Vincenzo Librandi, May 13 2011

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944