A393337 - OEIS

%I #7 Feb 17 2026 21:47:47

%S 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,

%T 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,

%U 1,2,0,0,0,1,1,3,0,0,1,23,1,0,1,0,0,2

%N Number of connected unlabeled graphs with composition number n.

%C See A392291 for the definition of composition number.

%C The null graph is not included.

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

%C 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).

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

%H Pontus von Brömssen, <a href="/A393337/b393337.txt">Table of n, a(n) for n = 1..256</a>

%H Pontus von Brömssen, <a href="/A393337/a393337.txt">Lists of all connected graphs (in graph6 format) with composition numbers 1-256</a>.

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

%K nonn

%O 1,8

%A _Pontus von Brömssen_, Feb 13 2026