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 1-3 of 3 results.

A079574 Number of unlabeled, connected graphs on n vertices with no induced subgraph isomorphic to a K_4, where a K_4 is the complete graph on four vertices.

Original entry on oeis.org

1, 1, 2, 5, 17, 82, 536, 5606, 95915, 2784072, 135885572, 10977061102, 1448150962596
Offset: 1

Views

Author

Jim Nastos, Jan 24 2003

Keywords

References

  • Inverse EULER transform of A304124.

Links

  • F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 332a754

Extensions

a(10) from the Encyclopedia of Finite Graphs (Travis Hoppe and Anna Petrone), Apr 11 2014
a(11) and a(12) added using tinygraph by Falk Hüffner, Jan 14 2016
a(13) from Brendan McKay, Jun 11 2021

A115196 Triangle read by rows formed from nonzero entries in table of number of graphs on n nodes with clique number k.

Original entry on oeis.org

1, 1, 2, 1, 3, 6, 1, 4, 15, 13, 1, 5, 30, 82, 37, 1, 6, 51, 301, 578, 106, 1, 7, 80, 842, 4985, 6021, 409, 1, 8, 117, 1995, 27107, 142276, 101267, 1896, 1, 9, 164, 4210, 112225, 1724440, 7269487, 2882460, 12171
Offset: 2

Views

Author

N. J. A. Sloane, based on email from Keith Briggs, Apr 03 2006

Keywords

Examples

			Table: number of graphs on n nodes with clique number k
n = .1...2...3...4....5....6.....7......8........9.......10.
k ----------------------------------------------------------
2....0...1...2...6...13...37...106....409.....1896....12171 = A052450
3....0...0...1...3...15...82...578...6021...101267..2882460 = A052451
4....0...0...0...1...4....30...301...4985...142276..7269487 = A052452
5....0...0...0...0...1....5.....51....842....27107..1724440 = A077392
6....0...0...0...0...0....1......6.....80.....1995...112225 = A077393
7....0...0...0...0...0....0......1......7......117.....4210 = A077394
8....0...0...0...0...0....0......0......1........8......164 = A205577
9....0...0...0...0...0....0......0......0........1........9 = A205578
10...0...0...0...0...0....0......0......0........0........1.

Links

Crossrefs

Cf. A287024, A263341. Partial column sums: A304124, A304125.

Formula

1+Sum_{k>=2} T(n,k) = A000088(n). - R. J. Mathar, May 06 2018

A304125 Number of simple graphs with n vertices which contain no K5 subgraph.

Original entry on oeis.org

1, 2, 4, 11, 33, 150, 986, 11416, 245440, 10164119, 793907916, 114150623175, 29709609171994
Offset: 1

Views

Author

Brendan McKay, May 06 2018

Keywords

Comments

The graphs do not need to be connected.

Crossrefs

Cf. A000088, A006785 (no K3), A115196 (graphs by clique number), A304124 (no K4).

Formula

a(n) = 1+A052450(n)+A052451(n)+A052452(n).

Extensions

a(13) from Brendan McKay, May 08 2018
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.