A393337 Number of connected unlabeled graphs with composition number n.

1, 1, 0, 1, 1, 0, 0, 2, 0, 1, 0, 1, 1, 0, 1, 3, 0, 0, 0, 3, 0, 0, 0, 1, 1, 2, 1, 0, 0, 1, 1, 6, 0, 2, 1, 0, 0, 1, 0, 8, 0, 0, 1, 0, 0, 0, 1, 4, 0, 3, 0, 8, 0, 1, 0, 0, 0, 1, 0, 4, 0, 3, 0, 11, 2, 0, 0, 5, 1, 2, 0, 0, 0, 1, 1, 3, 0, 0, 1, 23, 1, 0, 1, 0, 0, 2

Offset

1,8

Comments

See A392291 for the definition of composition number.

The null graph is not included.

a(n) > 0 if and only if n is in A392291.

Only graphs with at most A070939(n) vertices can contribute to a(n), because the composition number of a connected graph with k+1 vertices is at least 2^k (with equality if and only if the graph is a tree).

a(2^k) >= A000055(k+1), because a tree with k+1 vertices has composition number 2^k.

Links

Pontus von Brömssen, Table of n, a(n) for n = 1..256

Pontus von Brömssen, Lists of all connected graphs (in graph6 format) with composition numbers 1-256.

Crossrefs

Cf. A000055, A070939, A392291, A393338 (records), A393339 (indices of records).

Sequence in context: A236511 A235924 A391441 * A097304 A136745 A214157

Adjacent sequences: A393334 A393335 A393336 * A393338 A393339 A393340

Keyword

nonn

Author

Pontus von Brömssen, Feb 13 2026

Status

approved