A084269 Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes having chromatic number k, 1 <= k <= n.

1, 0, 1, 0, 1, 1, 0, 3, 2, 1, 0, 5, 12, 3, 1, 0, 17, 64, 26, 4, 1, 0, 44, 475, 282, 46, 5, 1, 0, 182, 5036, 5009, 809, 74, 6, 1, 0, 730, 80947, 149551, 27794, 1940, 110, 7, 1, 0, 4032, 2010328, 7694428, 1890221, 113272, 4125, 156, 8, 1, 0, 25598, 76115143, 667036310, 248580644, 14545025, 389583, 8040, 212, 9, 1

Offset: 0

Author

Eric W. Weisstein, May 24 2003

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  1;
  0,   1;
  0,   1,     1;
  0,   3,     2,      1;
  0,   5,    12,      3,     1;
  0,  17,    64,     26,     4,    1;
  0,  44,   475,    282,    46,    5,   1;
  0, 182,  5036,   5009,   809,   74,   6, 1;
  0, 730, 80947, 149551, 27794, 1940, 110, 7, 1;
  ...
		

Links

• Eric Weisstein's World of Mathematics, n-Chromatic Graph

Crossrefs

Row sums are A001349.

Columns k=3..7 are A126737, A126738, A126739, A126740, A241702.

Partial row sums include A005142, A076322, A076323, A076324, A076325, A076326, A076327, A076328.

Essentially the same table as A126736.

Cf. A084268 (not necessarily connected), A115597.

Extensions

a(37)-a(66) from Andrew Howroyd, Dec 02 2018