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 10 results.

A185133 Number of not necessarily connected 3-regular simple graphs on 2n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 1, 1, 4, 15, 71, 428, 3406, 34270, 418621, 5937051, 94782437, 1670327647, 32090011476, 666351752261, 14859579573845
Offset: 0

Views

Author

Jason Kimberley, Mar 21 2012

Keywords

Links

Crossrefs

Not necessarily connected k-regular simple graphs girth exactly 3: A198313 (any k), A185643 (triangle); fixed k: A026796 (k=2), this sequence (k=3), A185143 (k=4), A185153 (k=5), A185163 (k=6).
Not necessarily connected 3-regular simple graphs on 2n vertices with girth exactly g: A185130 (triangle); fixed g: this sequence (g=3), A185134 (g=4), A185135 (g=5), A185136 (g=6).

Formula

a(n) = A005638(n) - A185334(n).
a(n) = A006923(n) + A185033(n).

A185043 Number of disconnected 4-regular simple graphs on n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 8, 25, 88, 377, 2026, 13349, 104593, 930571, 9124627, 96699740, 1095467916, 13175254799, 167460501260, 2241576473025, 31510509517563, 464047467911837, 7143984462730072, 114749034352969037, 1919656978492976231
Offset: 0

Views

Author

Jason Kimberley, Feb 29 2012

Keywords

Links

Crossrefs

4-regular simple graphs with girth exactly 3: A184943 (connected), this sequence (disconnected), A185143 (not necessarily connected).
Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), A210703 (triangle); for fixed k: A185033 (k=3), this sequence (k=4), A185053 (k=5), A185063 (k=6).
Disconnected 4-regular simple graphs with girth exactly g: this sequence (g=3), A185044 (g=4).

Formula

a(n) = A033483(n) - A185244(n).

Extensions

Terms a(27)-a(31), due to the extension of A006820 by Andrew Howroyd, from Jason Kimberley, Mar 16 2020

A185053 Number of disconnected 5-regular simple graphs on 2n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 3, 66, 8029, 3484759, 2595985769, 2815099031409
Offset: 0

Views

Author

Jason Kimberley, Mar 10 2012

Keywords

Links

Crossrefs

Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), A210703 (triangle); for fixed k: A185033 (k=3), A185043 (k=4), this sequence (k=5), A185063 (k=6).

Formula

a(n) = A165655(n) - A185254(n).

A210703 Triangular array D(n,k) counting disconnected k-regular simple graphs on n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0, 0, 3, 0, 1, 0, 0, 4, 8, 3, 1, 0, 0, 5, 0, 8, 0, 0, 0, 6, 29, 25, 3, 1, 0, 0, 9, 0, 88, 0, 1, 0, 0, 10, 138, 377, 66, 5, 1, 0, 0, 13, 0, 2026, 0, 25, 0, 0, 0, 17, 774, 13349, 8029, 297, 5, 1, 0, 0, 21, 0, 104593, 0, 8199, 0, 1, 0, 0, 25, 5678, 930571, 3484759, 377004, 1562, 7, 1
Offset: 2

Views

Author

Jason Kimberley, Jan 21 2013

Keywords

Examples

			2: 0;
3: 0;
4: 0, 0;
5: 0, 0;
6: 0, 0, 1;
7: 0, 0, 1;
8: 0, 0, 1, 1;
9: 0, 0, 2, 0;
10: 0, 0, 2, 2, 1;
11: 0, 0, 3, 0, 1;
12: 0, 0, 4, 8, 3, 1;
13: 0, 0, 5, 0, 8, 0;
14: 0, 0, 6, 29, 25, 3, 1;
15: 0, 0, 9, 0, 88, 0, 1;
16: 0, 0, 10, 138, 377, 66, 5, 1;
17: 0, 0, 13, 0, 2026, 0, 25, 0;
18: 0, 0, 17, 774, 13349, 8029, 297, 5, 1;
19: 0, 0, 21, 0, 104593, 0, 8199, 0, 1;
20: 0, 0, 25, 5678, 930571, 3484759, 377004, 1562, 7, 1;
21: 0, 0, 33, 0, 9124627, 0, 22014143, 0, 100, 0;
22: 0, 0, 39, 53324, 96699740, 2595985769, 1493574756, 21617036, 10901, 9, 1;
23: 0, 0, 49, 0, 1095467916, 0, 114880777582, 0, 3470736, 0, 1;
24: 0, 0, 60, 622716, 13175254799, 2815099031409, 9919463450854, 733460349818, 1473822243, 88238, 11, 1;

Links

Crossrefs

The sum of the n-th row is A210713(n).
Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), this sequence (triangle); for a fixed k: A185033 (k=3), A185043 (k=4), A185053 (k=5), A185063 (k=6).

Formula

D(n,k) = A068933(n,k) - A185204(n,k) [the former is padded to be a tabl but the latter is a tabf].
D(n,k) = A185643(n,k) - A186733(n,k) [both are tabl but the result is tabf].

A185034 Number of disconnected 3-regular simple graphs on 2n vertices with girth exactly 4.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 2, 9, 35, 176, 1151, 10329, 120456, 1701834, 27500216, 492269472, 9599036308, 201954501535, 4555108534562
Offset: 0

Views

Author

Jason Kimberley, Feb 29 2012

Keywords

Links

Crossrefs

Disconnected k-regular simple graphs with girth exactly 4: this sequence (k=3), A185044 (k=4).
Disconnected 3-regular simple graphs with girth exactly g: A185033 (g=3), this sequence (g=4), A185035 (g=5), A185036 (g=6), A185037 (g=7).

Formula

a(n) = A185234(n) - A185235(n).

A210713 Number of disconnected regular simple graphs on n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 5, 4, 16, 13, 64, 98, 597, 2064, 22472, 112814, 4799607, 31138903, 4207941575, 115979716284, 13482672620149
Offset: 0

Views

Author

Jason Kimberley, Apr 02 2012

Keywords

Links

Crossrefs

This sequence is the row sum sequence of the triangle A210703.
Disconnected k-regular simple graphs with girth exactly 3: this sequence (any k), A210703 (triangle); for fixed k: A185033 (k=3), A185043 (k=4), A185053 (k=5), A185063 (k=6).

Formula

a(n) = A068932(n) - A185214(n).

A185035 Number of disconnected 3-regular simple graphs on 2n vertices with girth exactly 5.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 12, 67, 597, 7134, 107820, 1876672, 35924730, 741405102, 16356067055, 383931363314
Offset: 0

Views

Author

Jason Kimberley, Feb 29 2012

Keywords

Links

Crossrefs

Disconnected 3-regular simple graphs with girth exactly g: A185033 (g=3), A185034 (g=4), this sequence (g=5), A185036 (g=6), A185037 (g=7).

Formula

a(n) = A185235(n) - A185236(n).

A185036 Number of disconnected 3-regular simple graphs on 2n vertices with girth exactly 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, 98176518258
Offset: 0

Views

Author

Jason Kimberley, Feb 29 2012

Keywords

Links

Crossrefs

Disconnected 3-regular simple graphs with girth exactly g: A185033 (g=3), A185034 (g=4), A185035 (g=5), this sequence (g=6), A185037 (g=7).

Formula

a(n) = A185236(n) - A185237(n).

A185063 Number of disconnected 6-regular simple graphs on n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 25, 297, 8199, 377004, 22014143, 1493574756, 114880777582, 9919463450854
Offset: 0

Views

Author

Jason Kimberley, Mar 10 2012

Keywords

Links

Crossrefs

Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), A210703 (triangle); for fixed k: A185033 (k=3), A185043 (k=4), A185053 (k=5), this sequence (k=6).

Formula

a(n) = A165656(n) - A185264(n).

A185037 Number of disconnected 3-regular simple graphs on 2n vertices with girth exactly 7.

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, 3, 27, 609, 32237, 1885410, 101214661, 5025320937
Offset: 0

Views

Author

Jason Kimberley, Feb 29 2012

Keywords

Links

Crossrefs

Disconnected 3-regular simple graphs with girth exactly g: A185033 (g=3), A185034 (g=4), A185035 (g=5), A185036 (g=6), this sequence (g=7).

Formula

a(n) = A185237(n) - A185238(n).
Showing 1-10 of 10 results.

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

Content is available under The OEIS End-User License Agreement.