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 1-9 of 9 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

A128237 Number of n-node (unlabeled) graphs with girth 4.

Original entry on oeis.org

0, 1, 3, 15, 59, 296, 1604, 11303, 102108, 1250114, 20738069, 467523871, 14230096759, 581439661069, 31720637440030
Offset: 3

Views

Author

Keith Briggs, May 05 2007

Keywords

Crossrefs

Cf. A006785, A006787.
Cf. A128041, A128042, A128236-A128243.

Formula

a(n) = A006785(n) - A006787(n).

Extensions

Corrected and extended by Martin Fuller, May 01 2015

A128240 Number of n-node (unlabeled) connected graphs with girth 3.

Original entry on oeis.org

0, 0, 1, 3, 15, 93, 794, 10850, 259700, 11706739, 1006609723, 164058686415, 50335888444167, 29003487017067011, 31397381129017616776, 63969560112658419275907, 245871831682052901418048916
Offset: 1

Views

Author

Keith Briggs, May 05 2007

Keywords

Comments

Number of unlabeled, connected graphs on n vertices with at least one induced subgraph isomorphic to a K_3, where K_3 is the complete graph on three vertices (a triangle). - Travis Hoppe and Anna Petrone, Jun 01 2014

Links

Crossrefs

a(n) = A001349(n) - A024607(n).
Cf. A128041, A128042, A128236-A128243.

Extensions

Corrected and extended by Martin Fuller, May 01 2015
Information added by Falk Hüffner, Nov 27 2015

A128241 Number of n-node (unlabeled) connected graphs with girth 4.

Original entry on oeis.org

0, 1, 2, 11, 41, 220, 1243, 9368, 89049, 1135894, 19381407, 445505570, 13741579905, 566739127723, 31124921885829
Offset: 3

Views

Author

Keith Briggs, May 05 2007

Keywords

Crossrefs

Cf. A024607, A126757.
Cf. A128041, A128042, A128236-A128243.

Formula

a(n) = A024607(n) - A126757(n). - Martin Fuller, May 01 2015

Extensions

Corrected and extended by Martin Fuller, May 01 2015

A128238 Number of n-node (unlabeled) graphs with girth 5.

Original entry on oeis.org

0, 0, 1, 2, 8, 26, 101, 396, 1744, 8531, 47803, 308086, 2300756, 19909540, 199365557
Offset: 3

Views

Author

Keith Briggs, May 05 2007

Keywords

Crossrefs

Cf. A128041, A128042, A128236-A128243.

Programs

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

Extensions

Corrected and extended by Martin Fuller, May 01 2015

A128239 Number of n-node (unlabeled) graphs with girth 6.

Original entry on oeis.org

0, 0, 0, 1, 2, 9, 28, 107, 376, 1457, 5733, 24385, 110240, 540400, 2867847
Offset: 3

Views

Author

Keith Briggs, May 05 2007

Keywords

Crossrefs

Cf. A128041, A128042, A128236-A128243.

Programs

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

Extensions

Corrected and extended by Martin Fuller, May 01 2015

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 1-9 of 9 results.

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