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

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

2,3

Links

Table of n, a(n) for n=2..46.

Keith M. Briggs, Combinatorial Graph Theory

Eric Weisstein's World of Mathematics, Clique Number

Formula

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

Example

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.

Crossrefs

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

Sequence in context: A213941 A360858 A181511 * A093346 A115597 A325007

Adjacent sequences: A115193 A115194 A115195 * A115197 A115198 A115199

Keyword

nonn,tabl

Author

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

Status

approved