A369997 Irregular triangle read by rows: T(n,k) is the number of connected induced k-vertex subgraphs, up to isomorphism, of the hypercube graph of dimension n >= 0, 1 <= k <= 2^n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 3, 1, 1, 1, 1, 1, 3, 4, 9, 15, 31, 35, 40, 24, 18, 6, 4, 1, 1

Offset: 0

Author

Pontus von Brömssen, Feb 07 2024

Keywords

• nonn
• tabf
• more

Comments

In A369605, two isomorphic subgraphs may both be counted, namely if there is no automorphism of the hypercube graph that takes one to the other. The first difference is T(4,5) = 4 < A369605(4,5) = 5. The path with 5 vertices is an induced subgraph of the 4-dimensional hypercube in two inequivalent ways: one that is contained in a 3-dimensional subcube and one that is not.

Examples

			Triangle begins:
  1;
  1, 1;
  1, 1, 1, 1;
  1, 1, 1, 3, 2, 3,  1,  1;
  1, 1, 1, 3, 4, 9, 15, 31, 35, 40, 24, 18, 6, 4, 1, 1;
  ...
		

Crossrefs

Cf. A369605 (up to automorphisms of the hypercube), A369995 (not necessarily connected subgraphs), A369998 (row sums), A369999.