A115597 Triangle read by rows: let a(n,k) = number of graphs on n nodes with chromatic number k; T(n,k) = a(n,n-k), n >= 2, k=0..n-2.

1, 1, 2, 1, 3, 6, 1, 4, 16, 12, 1, 5, 31, 84, 34, 1, 6, 52, 318, 579, 87, 1, 7, 81, 867, 5366, 5721, 302, 1, 8, 118, 2028, 28722, 155291, 87381, 1118, 1, 9, 165, 4251, 115391, 1919895, 7855628, 2104349, 5478

Offset

2,3

Links

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

Keith M. Briggs, Combinatorial Graph Theory

Example

Table of values of a(n,k): number of graphs on n nodes with chromatic number k
n. = .1...2...3...4....5....6.....7......8........9.......10
k.----------------------------------------------------------
2....0...1...2...6...12...34....87....302.....1118.....5478... = A076278
3....0...0...1...3...16...84...579...5721....87381..2104349... = A076279
4....0...0...0...1....4...31...318...5366...155291..7855628... = A076280
5....0...0...0...0....1....5....52....867....28722..1919895... = A076281
6....0...0...0...0....0....1.....6.....81.....2028...115391... = A076282
7....0...0...0...0....0....0.....1......7......118.....4251
8....0...0...0...0....0....0.....0......1........8......165
9....0...0...0...0....0....0.....0......0........1........9
10...0...0...0...0....0....0.....0......0........0........1
Triangle begins:
1
1 2
1 3 6
1 4 16 12
1 5 31 84 34
1 6 52 318 579 87
1 7 81 867 5366 5721 302
1 8 118 2028 28722 155291 87381 1118
1 9 165 4251 115391 1919895 7855628 2104349 5478

Crossrefs

Cf. A076278, A076279, A076280, A076281, A076282.

Cf. A084268 (essentially the same sequence).

Sequence in context: A181511 A115196 A093346 * A325007 A103371 A325015

Adjacent sequences: A115594 A115595 A115596 * A115598 A115599 A115600

Keyword

nonn,tabl

Author

N. J. A. Sloane, based on email from Keith Briggs, Mar 14 2006

Status

approved