A263342 Irregular triangle read by rows: T(n,k) is the number of unlabeled graphs with n vertices containing exactly k non-isomorphic induced subgraphs, 1 <= n <= k < A370001(n).

1, 2, 2, 2, 2, 2, 5, 2, 2, 0, 1, 8, 4, 10, 7, 2, 2, 0, 0, 4, 4, 6, 6, 14, 16, 14, 22, 16, 20, 16, 10, 4, 2, 2, 0, 0, 0, 0, 4, 4, 4, 10, 8, 8, 16, 10, 20, 32, 42, 36, 40, 48, 74, 56, 68, 76, 60, 74, 72, 60, 72, 64, 26, 34, 14, 8, 2

Offset: 1

Author

Christian Stump, Oct 15 2015

Keywords

• nonn
• tabf

Comments

Row sums give A000088, n >= 1.

There are at most A000171(n) odd terms in the n-th row, because complementary graphs have the same number of induced subgraphs. - Pontus von Brömssen, Mar 09 2024

Examples

			Triangle begins:
  1;
  2;
  2,2;
  2,2,5,2;
  2,0,1,8,4,10,7,2;
  2,0,0,4,4,6,6,14,16,14,22,16,20,16,10,4,2;
  ...
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..279 (rows n = 1..9)
• FindStat - Combinatorial Statistic Finder, The number of induced subgraphs.

Crossrefs

Cf. A000088, A000171, A370001.

Formula

T(n,n) = 2 for n >= 2, because the empty graph and the complete graph are the only n-vertex graphs having only n non-isomorphic induced subgraphs. - Pontus von Brömssen, Mar 09 2024

Extensions

a(34) and beyond from Pontus von Brömssen, Mar 09 2024