A394474 Triangle read by rows: T(n,k) is the number of connected simple graphs on n labeled nodes having chromatic number k, 1 <= k <= n.

1, 0, 1, 0, 3, 1, 0, 19, 18, 1, 0, 195, 472, 60, 1, 0, 3031, 18855, 4652, 165, 1, 0, 67263, 1195456, 570181, 32942, 413, 1, 0, 2086099, 123301668, 115800030, 10161350, 198464, 980, 1, 0, 89224635, 20919866437, 39798752520, 5343292155, 144063090, 1089984, 2250, 1

Offset

1,5

Links

Sean A. Irvine, Table of n, a(n) for n = 1..78 (rows 1..12 flattened)

Eric Weisstein's World of Mathematics, k-Chromatic Graph.

Example

Triangle begins:
  1;
  0, 1;
  0, 3, 1;
  0, 19, 18, 1;
  0, 195, 472, 60, 1;
  ...

Crossrefs

Cf. A001187 (row sums), A084269 (unlabeled), A394473 (all simple graphs).

Cf. A084273 (k=3), A084274 (k=4), A084283 (k<=3), A084284 (k<=4), A084285 (k<=5), A084286 (k<=6).

Sequence in context: A110518 A246049 A316773 * A394559 A006837 A158782

Adjacent sequences: A394471 A394472 A394473 * A394475 A394478 A394479

Keyword

nonn,tabl,hard

Author

Sean A. Irvine, Mar 23 2026

Status

approved