login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A068933 Triangular array D(n, r) = number of disconnected r-regular graphs with n nodes, 0 <= r < n. 18
0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 2, 1, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, 0, 1, 1, 4, 2, 1, 0, 0, 0, 0, 0, 1, 0, 5, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 8, 9, 3, 1, 0, 0, 0, 0, 0, 0, 1, 0, 9, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 12, 31, 25, 3, 1, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,31

COMMENTS

A graph is called r-regular if every node has exactly r edges. Row sums give A068932.

LINKS

Jason Kimberley, Rows 1..23 of A068933 triangle, flattened.

Jason Kimberley, Disconnected regular graphs (with girth at least 3)

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g

FORMULA

D(n, r) = A051031(n, r) - A068934(n, r).

EXAMPLE

This sequence can be computed using the information in A068934. We'll abbreviate A068934(n, r) as C(n, r). To compute D(13, 4), note that the connected components of a 4-regular graph must have at least 5 elements. So a disconnected 13-node 4-regular graph must have two components and their sizes are either 8 and 5, or 7 and 6. So D(13, 4) = C(8, 4)*C(5, 4) + C(7, 4)*C(6, 4) = 6*1 + 2*1 = 8.

0;

1, 0;

1, 0, 0;

1, 1, 0, 0;

1, 0, 0, 0, 0;

1, 1, 1, 0, 0, 0;

1, 0, 1, 0, 0, 0, 0;

1, 1, 2, 1, 0, 0, 0, 0;

1, 0, 3, 0, 0, 0, 0, 0, 0;

1, 1, 4, 2, 1, 0, 0, 0, 0, 0;

1, 0, 5, 0, 1, 0, 0, 0, 0, 0, 0;

1, 1, 8, 9, 3, 1, 0, 0, 0, 0, 0, 0;

1, 0, 9, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0;

1, 1, 12, 31, 25, 3...

CROSSREFS

Cf. A051031, A068932, A068934.

Sequence in context: A321921 A236419 A114448 * A015472 A049816 A143542

Adjacent sequences:  A068930 A068931 A068932 * A068934 A068935 A068936

KEYWORD

nonn,tabl

AUTHOR

David Wasserman, Mar 08 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)