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 1-7 of 7 results.

A033483 Number of disconnected 4-valent (or quartic) graphs with n nodes.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 8, 25, 88, 378, 2026, 13351, 104595, 930586, 9124662, 96699987, 1095469608, 13175272208, 167460699184, 2241578965849, 31510542635443, 464047929509794, 7143991172244290, 114749135506381940, 1919658575933845129, 33393712487076999918, 603152722419661386031
Offset: 0

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Author

Ronald C. Read

Keywords

References

  • R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.

Links

Crossrefs

4-regular simple graphs: A006820 (connected), this sequence (disconnected), A033301 (not necessarily connected). - Jason Kimberley, Jan 08 2011
Disconnected regular simple graphs: A068932 (any degree), A068933 (triangular array), specified degree k: A165652 (k=2), A165653 (k=3), this sequence (k=4), A165655 (k=5), A165656 (k=6), A165877 (k=7), A165878 (k=8), A185293 (k=9), A185203 (k=10), A185213 (k=11).
Disconnected 4-regular simple graphs with girth at least g: this sequence (g=3), A185244 (g=4), A185245 (g=5), A185246 (g=6).

Programs

Formula

a(n) = A033301(n) - A006820(n) = Euler_transformation(A006820) - A006820.
a(n) = A068933(n, 4). - Jason Kimberley, Sep 27 2009 and Jan 08 2011

Extensions

Terms a(16)-a(18) from Martin Fuller, Dec 04 2006
Terms a(19)-a(26) from Jason Kimberley, Sep 27 2009 and Dec 30 2010
Terms a(27)-a(33), due to the extension of A006820 by Andrew Howroyd, from Jason Kimberley, Mar 12 2020

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

A185226 Number of disconnected 2-regular simple graphs on n vertices with girth at least 6.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 5, 5, 7, 8, 10, 11, 15, 16, 20, 23, 28, 31, 39, 43, 52, 59, 70, 79, 95, 106, 125, 142, 166, 187, 220, 247, 287, 325, 375, 423, 490, 551, 633, 715, 818, 921, 1055, 1186, 1352, 1522, 1729, 1943, 2208
Offset: 0

Views

Author

Jason Kimberley, Feb 22 2011

Keywords

Comments

Number of partitions of n with each part at least 6, and at least 2 parts.

Links

Crossrefs

Disconnected k-regular simple graphs with girth at least 6: A185216 (all k), A185206 (triangle); this sequence (k=2), A185236 (k=3), A185246 (k=4).
Disconnected 2-regular simple graphs with girth at least g: A165652 (g=3), A185224 (g=4), A185225 (g=5), this sequence (g=6), A185227 (g=7), A185228 (g=8), A185229 (g=9).

Programs

Formula

a(n) = A185326(n) - A185116(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).

A185236 Number of disconnected 3-regular simple graphs on 2n vertices with girth at least 6.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 6, 37, 432, 8119, 191254, 4855919, 127937854, 3482858263, 98176518259
Offset: 0

Views

Author

Jason Kimberley, Feb 22 2011

Keywords

Links

Crossrefs

Disconnected k-regular simple graphs with girth at least 6: A185216 (all k), A185206 (triangle); A185226 (k=2), this sequence (k=3), A185246 (k=4).

A185245 Number of disconnected 4-regular simple graphs on n vertices with girth at least 5.

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, 0, 0, 0, 0, 0, 0, 1, 2, 11, 147, 4215, 132741, 4419691, 141928589, 4339298225, 128489587646
Offset: 0

Views

Author

Jason Kimberley, Feb 22 2011

Keywords

Links

Crossrefs

Disconnected 4-regular simple graphs with girth at least g: A033483 (g=3), A185244 (g=4), this sequence (g=5), A185246 (g=6).

A185206 Triangular array D(n,k) counting disconnected k-regular simple graphs on n vertices with girth at least 6.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 0, 2, 1, 1, 3, 1, 0, 3, 1, 1, 5, 1, 0, 5, 1, 1, 7, 1, 0, 8, 1, 1, 10, 1, 0, 11, 1, 1, 15, 1, 0, 16, 1, 1, 20, 1, 0, 23, 1, 1, 28, 1, 1, 0, 31, 0, 1, 1, 39, 1, 1, 0, 43, 0, 1, 1, 52, 6, 1, 0, 59, 0, 1, 1, 70, 37, 1, 0, 79, 0
Offset: 1

Views

Author

Jason Kimberley, Nov 03 2012

Keywords

Examples

			1: 0;
2: 1;
3: 1;
4: 1, 1;
5: 1, 0;
6: 1, 1;
7: 1, 0;
8: 1, 1;
9: 1, 0;
10: 1, 1;
11: 1, 0;
12: 1, 1, 1;
13: 1, 0, 1;
14: 1, 1, 2;
15: 1, 0, 2;
16: 1, 1, 3;
17: 1, 0, 3;
18: 1, 1, 5;
19: 1, 0, 5;
20: 1, 1, 7;
21: 1, 0, 8;
22: 1, 1, 10;
23: 1, 0, 11;
24: 1, 1, 15;
25: 1, 0, 16;
26: 1, 1, 20;
27: 1, 0, 23;
28: 1, 1, 28, 1;
29: 1, 0, 31, 0;
30: 1, 1, 39, 1;
31: 1, 0, 43, 0;
32: 1, 1, 52, 6;
33: 1, 0, 59, 0;
34: 1, 1, 70, 37;
35: 1, 0, 79, 0;
36: 1, 1, 95, 432;
37: 1, 0, 106, 0;
38: 1, 1, 125, 8119;
39: 1, 0, 142, 0;
40: 1, 1, 166, 191254;
41: 1, 0, 187, 0;
42: 1, 1, 220, 4855919;
43: 1, 0, 247, 0;
44: 1, 1, 287, 127937854;
45: 1, 0, 325, 0;
46: 1, 1, 375, 3482858263;
47: 1, 0, 423, 0;
48: 1, 1, 490, 98176518259;
49: 1, 0, 551, 0;

Links

Crossrefs

Disconnected k-regular simple graphs with girth at least 6: A185216 (all k), this sequence (triangle); A185226 (k=2), A185236 (k=3), A185246 (k=4).
Showing 1-7 of 7 results.

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