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 17 results. Next

A186724 Number of connected regular graphs with n nodes and girth at least 4.

Original entry on oeis.org

1, 1, 1, 0, 1, 1, 2, 1, 4, 1, 10, 3, 37, 32, 340, 1608, 18020, 193907, 2867725, 32674058, 1581632114, 6705889824
Offset: 0

Views

Author

Jason Kimberley, Sep 04 2011

Keywords

Links

Crossrefs

Regular graphs, of any degree, with girth at least 4: this sequence (connected), A185214 (disconnected), A185314 (not necessarily connected).
Connected regular graphs of any degree with girth at least g: A005177 (g=3), this sequence (g=4), A186725 (g=5), A186726 (g=6), A186727 (g=7), A186728 (g=8), A186729 (g=9).
Connected k-regular simple graphs with girth at least 4: this sequence (any k), A186714 (triangle); specified degree k: A185114 (k=2), A014371 (k=3), A033886 (k=4), A058275 (k=5), A058276 (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9).

Formula

a(n) = sum of the n-th row of A186714.

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).

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

A185314 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 4.

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 4, 2, 7, 3, 14, 6, 44, 37, 350, 1616, 18042, 193919, 2867779, 32674078, 1581632332, 6705889886
Offset: 0

Views

Author

Jason Kimberley, May 23 2012

Keywords

Links

Crossrefs

Regular graphs, of any degree, with girth at least 4: A186724 (connected), A185214 (disconnected), this sequence (not-necessarily connected).
Not necessarily connected k-regular simple graphs with girth at least 4: this sequence (any k), A185304 (triangle); specified degree k: A008484 (k=2), A185334 (k=3), A185344 (k=4), A185354 (k=5), A185364 (k=6).
Not necessarily connected regular simple graphs with girth at least g: A005176 (g=3), this sequence (g=4), A185315 (g=5), A185316 (g=6), A185317 (g=7), A185318 (g=8), A185319 (g=9).

Formula

a(n) = A186724(n) + A185214(n).
a(n) is the sum of the n-th row of A185304.

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).

A185254 Number of disconnected 5-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, 1, 1, 8, 395, 407240, 1125431866, 3814677304834
Offset: 0

Views

Author

Jason Kimberley, Feb 22 and Nov 04 2011

Keywords

Links

Crossrefs

5-regular simple graphs on 2n vertices with girth at least 4: A058275 (connected), this sequence (disconnected), A185354 (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), this sequence (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).

A185216 Number of disconnected regular simple graphs on n vertices with girth at least 6.

Original entry on oeis.org

0, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 4, 3, 5, 4, 7, 6, 9, 9, 12, 12, 17, 17, 22, 24, 31, 32, 42, 44, 60, 60, 109, 80, 529, 107, 8246, 143, 191422, 188, 4856141, 248, 127938143, 326, 3482858640, 424, 98176518751, 552
Offset: 0

Views

Author

Jason Kimberley, Jun 21 2012

Keywords

Links

Crossrefs

Disconnected k-regular simple graphs with girth at least 6: this sequence (all k), A185206 (triangle); A185226 (k=2), A185236 (k=3), A185246 (k=4).
Disconnected regular graphs with girth at least g: A068932 (g=3), A185214 (g=4), A185215 (g=5), this sequence (g=6), A185217 (g=7).

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).
Showing 1-10 of 17 results. Next

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

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