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.

A128042 Triangle read by columns: number of n-node (unlabeled) connected graphs with girth k, for n >= 3, k >= 3.

Original entry on oeis.org

1, 3, 1, 15, 2, 1, 93, 11, 1, 1, 794, 41, 5, 1, 1, 10850, 220, 16, 6, 1, 1, 259700, 1243, 66, 17, 5, 1, 1, 11706739, 9368, 266, 69, 15, 6, 1, 1, 1006609723, 89049, 1235, 239, 58, 18, 6, 1, 1, 164058686415, 1135894, 6350, 962, 202, 74, 19, 7, 1, 1
Offset: 3

Views

Author

Keith Briggs, May 05 2007

Keywords

Examples

			Number of n-node (unlabeled) connected graphs with girth k:
.k..|.n=........3........4........5........6........7........8........9........10
---------------------------------------------------------------------------------
.0..|...........0........0........0........0........0........0........0.........0
.1..|...........0........0........0........0........0........0........0.........0
.2..|...........0........0........0........0........0........0........0.........0
.3..|...........1........3.......15.......93......794....10850...259700..11706739
.4..|...........0........1........2.......11.......41......220.....1243......9368
.5..|...........0........0........1........1........5.......16.......66.......266
.6..|...........0........0........0........1........1........6.......17........69
.7..|...........0........0........0........0........1........1........5........15
.8..|...........0........0........0........0........0........1........1.........6
.9..|...........0........0........0........0........0........0........1.........1
10..|...........0........0........0........0........0........0........0.........1
11..|...........0........0........0........0........0........0........0.........0

Links

Crossrefs

Sequences for k=3..6 are A128240, A128241, A128242, A128243.
Cf. A128041, A006787, A128236, A128237, A128238, A128239.
Cf. A325455 (circumference).

Programs

Extensions

Corrected and extended by Martin Fuller, May 01 2015

A128236 Number of n-node (unlabeled) graphs with girth 3.

Original entry on oeis.org

1, 4, 20, 118, 937, 11936, 272771, 11992996, 1018892793, 165089910412, 50502010570950, 29054155189364119, 31426485955571756316, 64001015703946097640927, 245935864153501211843554826
Offset: 3

Views

Author

Keith Briggs, May 05 2007

Keywords

Crossrefs

a(n) = A000088(n) - A006785(n).
Cf. A128041, A128042, A128237-A128243.

Extensions

Corrected and extended by Martin Fuller, May 01 2015

A128243 Number of n-node (unlabeled) connected graphs with girth 6.

Original entry on oeis.org

0, 0, 0, 1, 1, 6, 17, 69, 239, 962, 3864, 17049, 79607, 403758, 2209386, 13138818, 84841130, 595825731
Offset: 3

Views

Author

Keith Briggs, May 05 2007

Keywords

Crossrefs

Cf. A128041, A128042.
Cf. A128236, A128237, A128238, A128239, A128240, A128241, A128242.

Programs

  • nauty
    geng -ctfq $n | countg -qg6 --ng # Martin Fuller, May 03 2015

Extensions

Corrected and extended by Martin Fuller, May 01 2015
a(18)-a(20) added by Georg Grasegger, May 02 2023

A006787 Number of n-node graphs with no cycles of length less than 5.

Original entry on oeis.org

1, 2, 3, 6, 11, 23, 48, 114, 293, 869, 2963, 12066, 58933, 347498, 2455693, 20592932, 202724920, 2322206466, 30743624324, 468026657815, 8161170076257
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Includes graphs with no cycles at all as well as graphs with girth greater than 5.

References

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

Links

Crossrefs

Cf. A000066, A000088, A054760, A159847, A126757 (connected, inv. Eul. Transf.), A128236, A128237, A300705.

Formula

a(n) = A000088(n) - A128236(n) - A128237(n). - Andrew Howroyd, May 06 2021

Extensions

Definition corrected by Brendan McKay, Apr 27 2007
a(18)-a(19) (from the McKay reference) added by R. J. Mathar, Jun 17 2008
a(20)-a(21) from Brendan McKay, Mar 11 2018

A128242 Number of n-node (unlabeled) connected graphs with girth 5.

Original entry on oeis.org

0, 0, 1, 1, 5, 16, 66, 266, 1235, 6350, 37364, 251106, 1942085, 17287710, 177086792, 2084120446, 28125888087, 434318629496, 7657513894860
Offset: 3

Views

Author

Keith Briggs, May 05 2007

Keywords

Crossrefs

Cf. A128041, A128042.
Cf. A128236, A128237, A128238, A128239, A128240, A128241, A128243.

Programs

  • nauty
    geng -ctfq $n | countg -qg5 --ng # Martin Fuller, May 03 2015

Extensions

Corrected and extended by Martin Fuller, May 01 2015
a(18)-a(21) added by Georg Grasegger, May 02 2023
Showing 1-5 of 5 results.

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

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