The On-Line Encyclopedia of Integer Sequences (OEIS)

The OEIS is supported by the many generous donors to the OEIS Foundation.

Revision History for A167625

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A167625

Square array T(n,k), read by upward antidiagonals, counting isomorphism classes of k-regular multigraphs of order n, loops allowed.
(history; published version)

#17 by OEIS Server at Mon Mar 23 15:44:45 EDT 2020

LINKS

Andrew Howroyd, <a href="/A167625/b167625_1.txt">Table of n, a(n) for n = 1..378</a> (27 antidiagonals, first 19 antidiagonals from Jason Kimberley)

#16 by Alois P. Heinz at Mon Mar 23 15:44:45 EDT 2020

STATUS

proposed

approved

Discussion

Mon Mar 23

15:44

OEIS Server: Installed new b-file as b167625.txt.  Old b-file is now b167625_1.txt.

#15 by Andrew Howroyd at Mon Mar 23 15:30:49 EDT 2020

STATUS

editing

proposed

#14 by Andrew Howroyd at Mon Mar 23 15:30:11 EDT 2020

NAME

Square array T(n,k), read by upward antidiagonals, counting isomorphism classes of k-regular multigraphs of order n, loops allowed.

STATUS

proposed

editing

Discussion

Mon Mar 23

15:30

Andrew Howroyd: yes, this one is upwards!

#13 by Andrew Howroyd at Mon Mar 23 15:27:59 EDT 2020

STATUS

editing

proposed

Discussion

Mon Mar 23

15:29

Alois P. Heinz: upwards diagonals ...

#12 by Andrew Howroyd at Mon Mar 23 15:22:59 EDT 2020

COMMENTS

Terms may be computed without generating each graph by enumerating the number of graphs by degree sequence. A PARI program showing this technique for graphs with labeled vertices is given in A333467. Burnside's lemma can be used to extend this method to the unlabeled case. - Andrew Howroyd, Mar 23 2020

#11 by Andrew Howroyd at Mon Mar 23 13:51:25 EDT 2020

LINKS

J. S. Kimberley, Andrew Howroyd, <a href="/A167625/b167625_1.txt">Antidiagonals Table of Tn, a(n,k) for n+k in = 1..378</a> (27 antidiagonals, first 19</a>. antidiagonals from Jason Kimberley)

CROSSREFS

Cf. A333330 (loopless), A333397 (connected), A333467 (labeled).

#10 by Andrew Howroyd at Sun Mar 15 15:00:24 EDT 2020

EXAMPLE

Array begins:

==============================================

n\k | 0 1 2 3 4 5 6 7

----+-----------------------------------------

1 | 1 0 1 0 1 0 1 0 ...

2 | 1 1 2 2 3 3 4 4 ...

3 | 1 0 3 0 7 0 13 0 ...

4 | 1 1 5 8 20 32 66 101 ...

5 | 1 0 7 0 56 0 384 0 ...

6 | 1 1 11 31 187 727 3369 12782 ...

7 | 1 0 15 0 654 0 40365 0 ...

8 | 1 1 22 140 2705 42703 675368 8584767 ...

...

CROSSREFS

Column sequences: A000012 (k=0), A059841 (k=1), A41 A000041 (k=2), A129427 (k=3), A129429 (k=4), A129431 (k=5), A129433 (k=6), A129435 (k=7), A129437 (k=8).

Cf. A333330 (loopless).

STATUS

approved

editing

Discussion

Sun Mar 22

16:58

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A167625 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

#9 by T. D. Noe at Sat Oct 13 00:22:50 EDT 2012

STATUS

editing

approved

#8 by Jason Kimberley at Tue Oct 09 00:54:29 EDT 2012

AUTHOR

Jason Kimberley (_Jason. Kimberley(AT)newcastle.edu.au), _, Nov 07 2009

STATUS

approved

editing