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 1-8 of 8 results.

A005176 Number of regular graphs with n unlabeled nodes.

Original entry on oeis.org

1, 1, 2, 2, 4, 3, 8, 6, 22, 26, 176, 546, 19002, 389454, 50314870, 2942198546, 1698517037030, 442786966117636, 649978211591622812, 429712868499646587714, 2886054228478618215888598, 8835589045148342277802657274, 152929279364927228928025482936226, 1207932509391069805495173417972533120, 99162609848561525198669168653641835566774
Offset: 0

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Author

N. J. A. Sloane

Keywords

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Not necessarily connected simple regular graphs: A005176 (any degree), A051031 (triangular array), specified degree k: A000012 (k=0), A059841 (k=1), A008483 (k=2), A005638 (k=3), A033301 (k=4), A165626 (k=5), A165627 (k=6), A165628 (k=7), A180260 (k=8).
Simple regular graphs of any degree: A005177 (connected), A068932 (disconnected), this sequence (not necessarily connected).
Not necessarily connected regular simple graphs with girth at least g: this sequence (g=3), A185314 (g=4), A185315 (g=5), A185316 (g=6), A185317 (g=7), A185318 (g=8), A185319 (g=9).
Cf. A295193.

Formula

a(n) = A005177(n) + A068932(n). - David Wasserman, Mar 08 2002
Row sums of triangle A051031.

Extensions

More terms from David Wasserman, Mar 08 2002
a(15) and a(16) from Jason Kimberley, Sep 25 2009
Edited by Jason Kimberley, Jan 06 2011 and May 24 2012
a(17)-a(21) from Andrew Howroyd, Mar 08 2020
a(22)-a(24) from Andrew Howroyd, Apr 05 2020

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.

A185315 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 5.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 3, 2, 3, 2, 5, 3, 7, 4, 15, 6, 57, 8, 466, 12, 5801, 24, 91091, 3939, 1744378, 4132022, 163639295, 4018022192, 119026596500
Offset: 0

Views

Author

Jason Kimberley, Dec 12 2012

Keywords

Links

Crossrefs

Not necessarily connected k-regular simple graphs with girth at least 5: this sequence (any k), A185305 (triangle); specified degree k: A185325 (k=2), A185335 (k=3).
Not necessarily connected regular simple graphs with girth at least g: A005176 (g=3), A185314 (g=4), this sequence (g=5), A185316 (g=6), A185317 (g=7), A185318 (g=8), A185319 (g=9).

Formula

a(n) = A186725(n) + A185215(n).

A185316 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 6.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 3, 2, 3, 2, 3, 2, 4, 3, 6, 4, 7, 5, 13, 7, 42, 10, 398, 13, 7592, 18, 181251, 25, 4624534, 33, 122090591, 45, 3328930034, 61, 93990693977, 106
Offset: 0

Views

Author

Jason Kimberley, Dec 12 2012

Keywords

Links

Crossrefs

Not necessarily connected regular simple graphs with girth at least g: A005176 (g=3), A185314 (g=4), A185315 (g=5), this sequence (g=6), A185317 (g=7), A185318 (g=8), A185319 (g=9).

Formula

a(n) = A186726(n) + A185216(n).

A185318 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 8.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 2, 1, 3, 2, 3, 2, 3, 2, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 9, 8, 11, 11, 14, 14, 19, 18, 23, 24, 30, 31, 41, 40, 61, 52, 217, 67, 4416, 86, 266463, 111, 20807816, 141
Offset: 0

Views

Author

Jason Kimberley, Dec 18 2012

Keywords

Links

Crossrefs

Not necessarily connected regular simple graphs with girth at least g: A005176 (g=3), A185314 (g=4), A185315 (g=5), A185316 (g=6), A185317 (g=7), this sequence (g=8), A185319 (g=9).

Formula

a(n) = A186728(n) + A185218(n).

A185319 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 9.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 8, 10, 10, 13, 13, 16, 17, 20, 21, 26, 27, 32, 35, 41, 44, 52, 56, 65, 72, 82, 90, 104, 114, 130, 144, 163, 180, 205, 226, 255, 283, 336
Offset: 0

Views

Author

Jason Kimberley, Dec 19 2012

Keywords

Links

Crossrefs

Not necessarily connected regular simple graphs with girth at least g: A005176 (g=3), A185314 (g=4), A185315 (g=5), A185316 (g=6), A185317 (g=7), A185318 (g=8), this sequence (g=9).

Formula

a(n) = A186729(n) + A185219(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).

A198317 Number of, not necessarily connected, regular simple graphs on n vertices with girth exactly 7.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 4, 7, 5, 27, 7, 553, 10, 30379, 13, 1782854, 18, 95079100, 24, 4686063134, 32
Offset: 0

Views

Author

Jason Kimberley, Dec 18 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), this sequence (g=7), A198318 (g=8).

Formula

a(n) = A186747(n) + A210717(n).
a(n) = A185317(n) - A185318(n).
Showing 1-8 of 8 results.

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

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