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 1-5 of 5 results.

A198313 Number of, not necessarily connected, regular simple graphs on n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 4, 4, 15, 23, 162, 540, 18958, 389417, 50314520, 2942196930, 1698517018988
Offset: 0

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Author

Jason Kimberley, May 24 2012

Keywords

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Crossrefs

Not necessarily connected k-regular simple graphs girth exactly 3: this sequence (any k), A185643 (triangle); fixed k: A026796 (k=2), A185133 (k=3), A185143 (k=4), A185153 (k=5), A185163 (k=6).
Not necessarily connected regular simple graphs girth exactly g: this sequence (g=3), A198314 (g=4), A198315 (g=5), A198316 (g=6), A198317 (g=7), A198318 (g=8).

Formula

a(n) = A186743(n) + A210713(n).
a(n) = A005176(n) - A185314(n).
a(n) is the sum of the n-th row of A185643.

A198314 Number of, not necessarily connected, regular simple graphs on n vertices with girth exactly 4.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 1, 0, 4, 1, 8, 3, 37, 33, 335, 1610, 17985, 193911, 2867313, 32674066, 1581626531, 6705889862
Offset: 0

Views

Author

Jason Kimberley, Dec 12 2012

Keywords

Links

Crossrefs

Not necessarily connected k-regular simple graphs girth exactly 4: this sequence (any k), A185644 (triangle); fixed k: A026797 (k=2), A185134 (k=3), A185144 (k=4).
Not necessarily connected regular simple graphs girth exactly g: A198313 (g=3), this sequence (g=4), A198315 (g=5), A198316 (g=6), A198317 (g=7), A198318 (g=8).

Formula

a(n) = A186744(n) + A210714(n).
a(n) = A185314(n) - A185315(n).

Extensions

a(10) corrected from 9 to 8 by Jason Kimberley, Feb 22 2013

A198315 Number of, not necessarily connected, regular simple graphs on n vertices with girth exactly 5.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 3, 1, 9, 2, 50, 3, 453, 5, 5759, 14, 90693, 3926, 1736786, 4132004, 163458044, 4018022167, 119021971966
Offset: 0

Views

Author

Jason Kimberley, Dec 13 2012

Keywords

Links

Crossrefs

Not necessarily connected regular simple graphs girth exactly g: A198313 (g=3), A198314 (g=4), this sequence (g=5), A198316 (g=6), A198317 (g=7), A198318 (g=8).

Formula

a(n) = A186745(n) + A210715(n).
a(n) = A185315(n) - A185316(n).

A198316 Number of, not necessarily connected, regular simple graphs on n vertices with girth exactly 6.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 1, 7, 2, 35, 3, 389, 4, 7579, 6, 181233, 9, 4624493, 12, 122090019, 17, 3328899632, 24, 93988911093, 57
Offset: 0

Views

Author

Jason Kimberley, Dec 13 2012

Keywords

Links

Crossrefs

Not necessarily connected regular simple graphs girth exactly g: A198313 (g=3), A198314 (g=4), A198315 (g=5), this sequence (g=6), A198317 (g=7), A198318 (g=8).

Formula

a(n) = A186746(n) + A210716(n).
a(n) = A185316(n) - A185317(n).

A198318 Number of, not necessarily connected, regular simple graphs on n vertices with girth exactly 8.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 6, 5, 7, 7, 10, 10, 15, 13, 29, 17, 176, 23, 4364, 30, 266398, 39, 20807734, 51
Offset: 0

Views

Author

Jason Kimberley, Dec 19 2012

Keywords

Links

Crossrefs

Not necessarily connected regular simple graphs girth exactly g: A198313 (g=3), A198314 (g=4), A198315 (g=5), A198316 (g=6), A198317 (g=7), this sequence (g=8).

Formula

a(n) = A186748(n) + A210718(n).
a(n) = A185318(n) - A185319(n).
Showing 1-5 of 5 results.

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

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