A184164 List of numbers that are not the number of subtrees of some tree.

2, 4, 5, 7, 8, 9, 12, 13, 14, 16, 18, 19, 22, 23, 26, 27, 29, 31, 33, 35, 38, 39, 42, 43, 46, 50, 52, 54, 60, 65, 68, 72, 77, 89

Offset: 1

Author

Emeric Deutsch, Oct 19 2011

Keywords

• nonn
• fini
• full

Comments

This is a finite list of 34 numbers.

Examples

			4 and 5 are in the sequence since the 2-vertex tree has 3 subtrees and an m-vertex tree (m>=3) has at least 6 subtrees.
		

Links

• Éva Czabarka, László Székely, and Stephan Wagner, The inverse problem for certain tree parameters, Discrete Appl. Math., 157, 2009, 3314-3319, section 2.6.
• Ryan McCulloch, Brendan D. McKay, Alireza Salahshoori, and Thomas Zaslavsky, The Cycle Counts of Graphs, arXiv:2507.02260 [math.CO], 2025. See p. 7.

Crossrefs

Cf. A344406 (caterpillars).