cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 12 results. Next

A058275 Number of connected 5-regular simple graphs on 2*n vertices with girth at least 4.

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 1, 7, 388, 406824, 1125022325, 3813549359274
Offset: 0

Views

Author

N. J. A. Sloane, Dec 17 2000

Keywords

Comments

The null graph on 0 vertices is vacuously connected and 5-regular; since it is acyclic, it has infinite girth. - Jason Kimberley, Jan 30 2011

References

  • M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146. - Jason Kimberley, Jan 30 2011

Links

Crossrefs

From Jason Kimberley, Jan 30 and Nov 04 2011: (Start)
5-regular simple graphs on 2n vertices with girth at least 4: this sequence (connected), A185254 (disconnected), A185354 (not necessarily connected).
Connected k-regular simple graphs with girth at least 4: A186724 (any k), A186714 (triangle); specified degree k: A185114 (k=2), A014371 (k=3), A033886 (k=4), this sequence (k=5), A058276 (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9).
Connected 5-regular simple graphs with girth at least g: A006821 (g=3), this sequence (g=4), A205295 (g=5).
Connected 5-regular simple graphs with girth exactly g: A184953 (g=3), A184954 (g=4), A184955 (g=5). (End)

Formula

a(n) = A185354(n) - A185254(n);
This sequence is the inverse Euler transformation of A185354. - Jason Kimberley, Nov 04 2011

Extensions

Terms a(10) and a(11) appended, from running Meringer's GENREG for 3.8 and 7886 processor days at U. Ncle., by Jason Kimberley on Jun 28 2010

A185224 Number of disconnected 2-regular simple graphs on n vertices with girth at least 4.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 6, 7, 10, 11, 15, 17, 23, 26, 33, 38, 49, 56, 69, 80, 99, 114, 139, 160, 194, 224, 268, 310, 370, 426, 504, 582, 687, 790, 927, 1066, 1247, 1433, 1667, 1913, 2222, 2545, 2944, 3369, 3888, 4442, 5112, 5833, 6697, 7631, 8739
Offset: 0

Views

Author

Jason Kimberley, Feb 22 2011

Keywords

Comments

a(n) is also the number of partitions of n with each part at least 4 and at most n-1. The integer i corresponds to the i-cycle; addition of integers corresponds to disconnected union of cycles.

Links

Crossrefs

2-regular graphs with girth at least 4: A185114 (connected), this sequence (disconnected), A008484 (not necessarily connected).
Disconnected k-regular simple graphs with girth at least 4: A185214 (any k), A185204 (triangle); specified degree k: A185224 (k=2), A185234 (k=3), A185244 (k=4), A185254 (k=5), A185264 (k=6), A185274 (k=7), A185284 (k=8), A185294 (k=9).
Disconnected 2-regular simple graphs with girth at least g [partitions of n with each part i being g <= i < n]: A165652 (g=3), this sequence (g=4), A185225 (g=5), A185226 (g=6), A185227 (g=7), A185228 (g=8), A185229 (g=9).

Programs

Formula

a(n) = A008484(n) - A185114(n).

A185214 Number of disconnected regular simple graphs on n vertices with girth at least 4.

Original entry on oeis.org

0, 0, 1, 1, 2, 1, 2, 1, 3, 2, 4, 3, 7, 5, 10, 8, 22, 12, 54, 20, 218, 62, 1436, 1731, 27810, 197981, 2613814, 33117962, 463707741, 6709514340, 102306352539, 1597440872801
Offset: 0

Views

Author

Jason Kimberley, Mar 26 2012

Keywords

Links

Crossrefs

This sequence is the row sum sequence of A185204.
Regular graphs, of any degree, with girth at least 4: A186724 (connected), this sequence (disconnected), A185314 (not necessarily connected).
Disconnected k-regular simple graphs with girth at least 4: this sequence (any k), A185204 (triangle); specified degree k: A185224 (k=2), A185234 (k=3), A185244 (k=4), A185254 (k=5), A185264 (k=6), A185274 (k=7), A185284 (k=8), A185294 (k=9).

Extensions

a(31) corrected by the author, propagated from A185244, Jan 05 2013

A185244 Number of disconnected 4-regular simple graphs on n vertices with girth at least 4.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 15, 35, 247, 1692, 17409, 197924, 2492824, 33117880, 461597957, 6709514218, 101153412903, 1597440868898
Offset: 0

Views

Author

Jason Kimberley, Feb 22 2011

Keywords

Links

Crossrefs

4-regular simple graphs with girth at least 4: A033886 (connected), this sequence (disconnected), A185344 (not necessarily connected).
Disconnected 4-regular simple graphs with girth at least g: A033483 (g=3), this sequence (g=4), A185245 (g=5), A185246 (g=6).
Disconnected k-regular simple graphs with girth at least 4: A185214 (any k), A185204 (triangle); specified degree k: A185224 (k=2), A185234 (k=3), this sequence (k=4), A185254 (k=5), A185264 (k=6), A185274 (k=7), A185284 (k=8), A185294 (k=9).

Formula

a(n) = A185344(n) - A033886(n) = Euler_transformation(A033886)(n) - A033886(n).
a(n) = A185044(n) + A185245(n).

Extensions

a(31) appended by the author once A033886(23) was known, Nov 03 2011
a(31) corrected by the author, Jan 05 2013

A185204 Triangular array D(n,k) counting disconnected k-regular simple graphs on n vertices with girth at least 4.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 0, 2, 1, 1, 4, 1, 1, 0, 4, 0, 1, 1, 6, 2, 1, 0, 7, 0, 1, 1, 10, 9, 1, 1, 0, 11, 0, 0, 1, 1, 15, 35, 2, 1, 0, 17, 0, 2, 1, 1, 23, 177, 15, 1, 1, 0, 26, 0, 35, 0, 1, 1, 33, 1153, 247, 1, 1, 0, 38, 0, 1692, 0, 1, 1, 49, 10341, 17409, 8, 1
Offset: 1

Views

Author

Jason Kimberley, Feb 22 2011

Keywords

Comments

For n >= 0 and 0 <= k <= A002265(n).

Examples

			0;
1;
1;
1, 1;
1, 0;
1, 1;
1, 0;
1, 1, 1;
1, 0, 1;
1, 1, 2;
1, 0, 2;
1, 1, 4, 1;
1, 0, 4, 0;
1, 1, 6, 2;
1, 0, 7, 0;
1, 1, 10, 9, 1;
1, 0, 11, 0, 0;
1, 1, 15, 35, 2;
1, 0, 17, 0, 2;

Links

Crossrefs

Disconnected k-regular simple graphs with girth at least 4: A185214 (any k), this sequence (triangle); specified degree k: A185224 (k=2), A185234 (k=3), A185244 (k=4), A185254 (k=5), A185264 (k=6), A185274 (k=7), A185284 (k=8), A185294 (k=9).

Extensions

The b-file corrected and a-file expanded by the author, Jan 19 2013

A185234 Number of disconnected 3-regular simple graphs on 2n vertices with girth at least 4.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 2, 9, 35, 177, 1153, 10341, 120523, 1702432, 27507351, 492377298, 9600913017, 201990426697, 4555849947783
Offset: 0

Views

Author

Jason Kimberley, Feb 22 2011

Keywords

Links

Crossrefs

Disconnected k-regular simple graphs with girth at least 4: A185214 (any k), A185204 (triangle); specified degree k: A185224 (k=2), this sequence (k=3), A185244 (k=4), A185254 (k=5), A185264 (k=6), A185274 (k=7), A185284 (k=8), A185294 (k=9).

A185264 Number of disconnected 6-regular simple graphs on n vertices with girth at least 4.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 10, 7, 277, 3742, 483330, 69827771, 14836620025
Offset: 0

Views

Author

Jason Kimberley, Feb 22 2011

Keywords

Links

Crossrefs

6-regular simple graphs with girth at least 4: A058276 (connected), this sequence (disconnected), A185364 (not necessarily connected).
Disconnected k-regular simple graphs with girth at least 4: A185214 (any k), A185204 (triangle); specified degree k: A185224 (k=2), A185234 (k=3), A185244 (k=4), A185254 (k=5), this sequence (k=6), A185274 (k=7), A185284 (k=8), A185294 (k=9).

Formula

a(n)
= A185364(n) - A058276(n)
= Euler_transformation(A058276)(n) - A058276(n).

A185274 Number of disconnected 7-regular simple graphs on 2n vertices with girth at least 4.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 9, 749, 2888270
Offset: 0

Views

Author

Jason Kimberley, Feb 22 2011

Keywords

Links

Crossrefs

Disconnected k-regular simple graphs with girth at least 4: A185214 (any k), A185204 (triangle); specified degree k: A185224 (k=2), A185234 (k=3), A185244 (k=4), A185254 (k=5), A185264 (k=6), this sequence (k=7), A185284 (k=8), A185294 (k=9).

A185284 Number of disconnected 8-regular simple graphs on n vertices with girth at least 4.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 14, 1
Offset: 0

Views

Author

Jason Kimberley, Feb 22 2011

Keywords

Links

Crossrefs

Disconnected k-regular simple graphs with girth at least 4: A185214 (any k), A185204 (triangle); specified degree k: A185224 (k=2), A185234 (k=3), A185244 (k=4), A185254 (k=5), A185264 (k=6), A185274 (k=7), this sequence (k=8), A185294 (k=9).

A185294 Number of disconnected 9-regular simple graphs on 2n vertices with girth at least 4.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 15
Offset: 0

Views

Author

Jason Kimberley, Feb 22 2011

Keywords

Links

Crossrefs

Disconnected k-regular simple graphs with girth at least 4: A185214 (any k), A185204 (triangle); specified degree k: A185224 (k=2), A185234 (k=3), A185244 (k=4), A185254 (k=5), A185264 (k=6), A185274 (k=7), A185284 (k=8), this sequence (k=9).
Showing 1-10 of 12 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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