cp's OEIS Frontend

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

%I A115196 #15 Feb 16 2025 08:33:00
%S A115196 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,
%T A115196 4985,6021,409,1,8,117,1995,27107,142276,101267,1896,1,9,164,4210,
%U A115196 112225,1724440,7269487,2882460,12171
%N A115196 Triangle read by rows formed from nonzero entries in table of number of graphs on n nodes with clique number k.
%H A115196 Keith M. Briggs, <a href="http://keithbriggs.info/cgt.html">Combinatorial Graph Theory</a>
%H A115196 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CliqueNumber.html">Clique Number</a>
%F A115196 1+Sum_{k>=2} T(n,k) = A000088(n). - _R. J. Mathar_, May 06 2018
%e A115196 Table: number of graphs on n nodes with clique number k
%e A115196 n = .1...2...3...4....5....6.....7......8........9.......10.
%e A115196 k ----------------------------------------------------------
%e A115196 2....0...1...2...6...13...37...106....409.....1896....12171 = A052450
%e A115196 3....0...0...1...3...15...82...578...6021...101267..2882460 = A052451
%e A115196 4....0...0...0...1...4....30...301...4985...142276..7269487 = A052452
%e A115196 5....0...0...0...0...1....5.....51....842....27107..1724440 = A077392
%e A115196 6....0...0...0...0...0....1......6.....80.....1995...112225 = A077393
%e A115196 7....0...0...0...0...0....0......1......7......117.....4210 = A077394
%e A115196 8....0...0...0...0...0....0......0......1........8......164 = A205577
%e A115196 9....0...0...0...0...0....0......0......0........1........9 = A205578
%e A115196 10...0...0...0...0...0....0......0......0........0........1.
%Y A115196 Cf. A287024, A263341. Partial column sums: A304124, A304125.
%K A115196 nonn,tabl
%O A115196 2,3
%A A115196 _N. J. A. Sloane_, based on email from _Keith Briggs_, Apr 03 2006