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 11-13 of 13 results.

A185364 Not necessarily connected 6-regular simple graphs on n vertices with girth at least 4.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 9, 6, 267, 3727, 483012, 69823723, 14836130862
Offset: 0

Views

Author

Jason Kimberley, Dec 07 2011

Keywords

Comments

First differs from A058276 at n=24.

Crossrefs

6-regular simple graphs with girth at least 4: A058276 (connected), A185264 (disconnected), this sequence (not necessarily connected).
Not necessarily connected k-regular simple graphs with girth at least 4: A185314 (any k), A185304 (triangle); specified degree k: A008484 (k=2), A185334 (k=3), A185344 (k=4), A185354 (k=5), this sequence (k=6).
Cf. A184964.

Programs

Formula

This sequence is the Euler transformation of A058276.
a(n) = A058276(n) + A185264(n).

A185336 Number of not necessarily connected 3-regular simple graphs on 2n vertices with girth at least 6.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 1, 1, 5, 32, 385, 7574, 181227, 4624502, 122090545, 3328929960, 93990692632, 2754222605808
Offset: 0

Views

Author

Jason Kimberley, Jan 28 2012

Keywords

Comments

The null graph on 0 vertices is vacuously 3-regular; since it is acyclic, it has infinite girth.

Crossrefs

3-regular simple graphs with girth at least 6: A014374 (connected), A185236 (disconnected), this sequence (not necessarily connected).
Not necessarily connected k-regular simple graphs with girth at least 6: A185326 (k=2), this sequence (k=3).
Not necessarily connected 3-regular simple graphs with girth *at least* g: A005638 (g=3), A185334 (g=4), A185335 (g=5), this sequence (g=6).
Not necessarily connected 3-regular simple graphs with girth *exactly* g: A185133 (g=3), A185134 (g=4), A185135 (g=5), A185136 (g=6).

Programs

  • Mathematica
    A014374 = Cases[Import["https://oeis.org/A014374/b014374.txt", "Table"], {, }][[All, 2]];
    etr[f_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d f[d], {d, Divisors[j]}] b[n - j], {j, 1, n}]/n]; b];
    a = etr[A014374[[# + 1]]&];
    a /@ Range[0, Length[A014374] - 1] (* Jean-François Alcover, Dec 04 2019 *)

Formula

Euler transformation of A014374.

Extensions

a(18) from A014374 from Jean-François Alcover, Dec 04 2019

A185330 Irregular triangle E(n,g) counting not necessarily connected 3-regular simple graphs on 2n vertices with girth at least g.

Original entry on oeis.org

1, 2, 1, 6, 2, 21, 6, 1, 94, 23, 2, 540, 112, 9, 1, 4207, 801, 49, 1, 42110, 7840, 455, 5, 516344, 97723, 5784, 32, 7373924, 1436873, 90940, 385, 118573592, 23791155, 1620491, 7574, 1, 2103205738, 432878091, 31478651, 181227, 3, 40634185402
Offset: 2

Views

Author

Jason Kimberley, Oct 18 2012

Keywords

Comments

The first column is for girth at least 3. The row length is incremented to g-2 when 2n reaches A000066(g).

Examples

			1;
2, 1;
6, 2;
21, 6, 1;
94, 23, 2;
540, 112, 9, 1;
4207, 801, 49, 1;
42110, 7840, 455, 5;
516344, 97723, 5784, 32;
7373924, 1436873, 90940, 385;
118573592, 23791155, 1620491, 7574, 1;
2103205738, 432878091, 31478651, 181227, 3;
40634185402, 8544173926, 656784488, 4624502, 21;
847871397424, 181519645163, 14621878339, 122090545, 546, 1;
18987149095005, 4127569521160, 345975756388, 3328929960, 30368, 0;
		

Crossrefs

Previous Showing 11-13 of 13 results.