A394473 Triangle read by rows: T(n,k) is the number of simple graphs on n labeled nodes having chromatic number k, 1 <= k <= n.

1, 1, 1, 1, 6, 1, 1, 40, 22, 1, 1, 375, 582, 65, 1, 1, 5176, 22377, 5042, 171, 1, 1, 103236, 1353810, 605545, 34139, 420, 1, 1, 2922445, 134222308, 120653315, 10434574, 201824, 988, 1, 1, 116011230, 22133512793, 40885736829, 5437235073, 145879674, 1098876, 2259, 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;
  1, 1;
  1, 6, 1;
  1, 40, 22, 1;
  1, 375, 582, 65, 1;
  ...

Crossrefs

Cf. A006125 (row sums), A084268 (unlabeled), A394474 (connected).

Cf. A084270 (k=2), A084271 (k=3), A084272 (k=4).

Sequence in context: A203338 A158116 A172343 * A395684 A058875 A156764

Adjacent sequences: A394470 A394471 A394472 * A394474 A394475 A394478

Keyword

nonn,tabl,hard

Author

Sean A. Irvine, Mar 21 2026

Status

approved