The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A191646 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
newer changes | Showing entries 11-20 | older changes

A191646

Triangle read by rows: T(n,k) = number of connected multigraphs with n >= 0 edges and 1 <= k <= n+1 vertices, with no loops allowed.
(history; published version)

#60 by Petros Hadjicostas at Thu Oct 03 02:18:07 EDT 2019

LINKS

Brendan McKay and Adolfo Piperno

STATUS

proposed

editing

#59 by Michel Marcus at Thu Oct 03 02:16:17 EDT 2019

STATUS

editing

proposed

#58 by Michel Marcus at Thu Oct 03 02:16:09 EDT 2019

LINKS

nauty and Traces, <a href="http://users.cecs.anu.edu.au/~bdm/nauty/">nauty 2.4</a>

Numbers in this table were computed using <a href="http://users.cecs.anu.edu.au/~bdm/nauty/">nauty 2.4</a>

STATUS

proposed

editing

#57 by Petros Hadjicostas at Wed Oct 02 14:57:28 EDT 2019

STATUS

editing

proposed

Discussion

Thu Oct 03

02:16

Petros Hadjicostas: By looking at the roots of the denominators of o.g.f. of columns k = 3 and k = 4 of A191646, I suspect that the general case involves quasi-polynomials in the sense of Lysonek (2007) (only roots of the denominator are roots of unity). One day I will find the appropriate paper that contains the general solution... it should be out there...

#56 by Petros Hadjicostas at Wed Oct 02 14:56:18 EDT 2019

FORMULA

T(n,k=3) = A253186(n) = A034253(n,k=2) for n >= 1. - Petros Hadjicostas, Oct 02 2019

#55 by Petros Hadjicostas at Wed Oct 02 14:55:43 EDT 2019

CROSSREFS

Cf. A034253, A054923, A192517, A253186 (column k=3), A290778 (column k=4).

#54 by Petros Hadjicostas at Wed Oct 02 14:55:07 EDT 2019

FORMULA

T(n,k=3) = A253186(n) = A034253(n,k=2) for n >= 1. - Petros Hadjicostas, Oct 02 2019

#53 by Petros Hadjicostas at Wed Oct 02 14:53:05 EDT 2019

NAME

Triangle read by rows: T(n,k) = number of connected multigraphs with n >= 0 edges and 1 <= k <= n+1 vertices, with no loops allowed.

LINKS

R. J. Mathar, <a href="http://arxiv.org/abs/1709.09000">Statistics on Small Graphs</a>, arXiv:1709.09000 [math.CO] (, 2017), ; see Section 4.

#52 by Petros Hadjicostas at Wed Oct 02 14:48:54 EDT 2019

LINKS

Gus Wiseman, <a href="/A191646/a191646.png">Illustration of the 33 connected multigraphs counted in row 5.</a>.

EXAMPLE

Triangle T(n,k) (with rows n >= 0 and columns k >= 1) begins as follows:

1;

0, 1;

0, 1, 1;

0, 1, 2, 2;

0, 1, 3, 5, 3;

0, 1, 4, 11, 11, 6;

0, 1, 6, 22, 34, 29, 11;

...

STATUS

approved

editing

#51 by Susanna Cuyler at Thu Nov 29 09:21:37 EST 2018

STATUS

proposed

approved