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.

Previous Showing 11-14 of 14 results.

A006925 Number of connected trivalent graphs with 2n nodes and girth exactly 5.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 2, 8, 48, 450, 5751, 90553, 1612905, 31297357, 652159389, 14499780660, 342646718608
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • CRC Handbook of Combinatorial Designs, 1996, p. 647.
  • Gordon Royle, personal communication.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Connected k-regular simple graphs with girth exactly 5: this sequence (k=3), A184945 (k=4), A184955 (k=5).
Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); specified g: A006923 (g=3), A006924 (g=4), this sequence
(g=5), A006926 (g=6), A006927 (g=7).
Connected 3-regular simple graphs with girth at least g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).

Formula

a(n) = A014372(n) - A014374(n).

Extensions

Definition corrected to include "connected", and "girth at least 5" minus "girth at least 6" formula provided by Jason Kimberley, Dec 12 2009

A006927 Number of connected trivalent graphs with 2n nodes and girth exactly 7.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 21, 545, 30368, 1782839, 95079080, 4686063107
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

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

Links

Crossrefs

Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); specified g: A006923 (g=3), A006924 (g=4), A006925 (g=5), A006926 (g=6), this sequence (g=7).
Connected 3-regular simple graphs with girth at least g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).

Formula

a(n) = A014375(n) - A014376(n).

Extensions

Definition amended to include "connected" (no disconnected yet), and "girth at least 7" minus "girth at least 8" formula provided by Jason Kimberley, Dec 12 2009

A185136 Number of not necessarily connected 3-regular simple graphs on 2n vertices with girth exactly 6.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 32, 385, 7573, 181224, 4624481, 122089999, 3328899592, 93988909792
Offset: 0

Views

Author

Jason Kimberley, Mar 21 2012

Keywords

Links

Crossrefs

Not necessarily connected 3-regular simple graphs on 2n vertices with girth exactly g: A185130 (triangle); fixed g: A185133 (g=3), A185134 (g=4), A185135 (g=5), this sequence (g=6).

Formula

a(n) = A006926(n) + A185036(n).

A210709 Number of trivalent connected simple graphs with 2n nodes and girth at least 9.

Original entry on oeis.org

1, 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, 18
Offset: 0

Views

Author

Jason Kimberley, Dec 20 2012

Keywords

Links

Crossrefs

Trivalent simple graphs with girth at least g: A185131 (triangle); chosen g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8), this sequence (g=9).
Trivalent simple graphs with girth exactly g: A198303 (triangle); chosen g: A006923 (g=3), A006924 (g=4), A006925 (g=5), A006926 (g=6), A006927 (g=7).

Formula

a(29) = a(A000066(9)/2) = A052453(9) = 18 is the number of (3,9) cages.
Previous Showing 11-14 of 14 results.

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

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