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

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

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).

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).

A185304 Triangular array E(n,k) counting not necessarily connected k-regular simple graphs on n vertices with girth at least 4.

Original entry on oeis.org

1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 2, 2, 1, 1, 0, 2, 0, 0, 1, 1, 3, 6, 2, 1, 1, 0, 3, 0, 2, 0, 1, 1, 5, 23, 12, 1, 1, 1, 0, 5, 0, 31, 0, 0, 1, 1, 7, 112, 220, 7, 1, 1, 1, 0, 8, 0, 1606, 0, 1, 0, 1, 1, 11, 801, 16829, 388, 9, 1, 1, 1, 0, 12, 0, 193900, 0, 6, 0, 0, 1, 1, 16, 7840, 2452820, 406824, 267, 8, 1, 1, 1, 0, 18, 0, 32670332, 0, 3727, 0, 0, 0
Offset: 1

Views

Author

Jason Kimberley, Jan 19 2013

Keywords

Comments

Row sums give A185314.

Examples

			1: 1;
2: 1, 1;
3: 1, 0;
4: 1, 1, 1;
5: 1, 0, 1;
6: 1, 1, 1, 1;
7: 1, 0, 1, 0;
8: 1, 1, 2, 2, 1;
9: 1, 0, 2, 0, 0;
10: 1, 1, 3, 6, 2, 1;
11: 1, 0, 3, 0, 2, 0;
12: 1, 1, 5, 23, 12, 1, 1;
13: 1, 0, 5, 0, 31, 0, 0;
14: 1, 1, 7, 112, 220, 7, 1, 1;
15: 1, 0, 8, 0, 1606, 0, 1, 0;
16: 1, 1, 11, 801, 16829, 388, 9, 1, 1;
17: 1, 0, 12, 0, 193900, 0, 6, 0,0;
18: 1, 1, 16, 7840, 2452820, 406824, 267, 8, 1, 1;
19: 1, 0, 18, 0, 32670332, 0, 3727, 0,0, 0;
20: 1, 1, 24, 97723, 456028489, 1125022326, 483012, 741, 13, 1, 1;
21: 1, 0, 27, 0, 6636066134, 0, 69823723, 0, 1, 0, 0;
22: 1, 1, 34, 1436873, 100135577994, 3813549359275, 14836130862, 2887493, ?, 14, 1;

Links

Crossrefs

Not necessarily connected k-regular simple graphs with girth at least 4: A185314 (any k), this sequence (triangle); specified degree k: A008484 (k=2), A185334 (k=3), A185344 (k=4), A185354 (k=5), A185364 (k=6).

Formula

E(n,k) = A186714(n,k) + A185204(n,k).

Extensions

E(10,2) corrected by the author, Mar 26 2013
a(32)=E(10,2) in b-file corrected as above by Andrew Howroyd, Feb 22 2018
Showing 1-10 of 12 results. Next

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