The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A054581 Number of unlabeled 2-trees with n nodes. 28
 1, 1, 1, 2, 5, 12, 39, 136, 529, 2171, 9368, 41534, 188942, 874906, 4115060, 19602156, 94419351, 459183768, 2252217207, 11130545494, 55382155396, 277255622646, 1395731021610, 7061871805974, 35896206800034, 183241761631584 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A 2-tree is recursively defined as follows: K_2 is a 2-tree and any 2-tree on n+1 vertices is obtained by joining a vertex to a 2-clique in a 2-tree on n vertices. Care is needed with the term 2-tree (and k-tree in general) because it has at least two commonly used definitions. A036361 gives the labeled version of this sequence, which has an easy formula analogous to Cayley's formula for the number of trees. Also, number of unlabeled 3-gonal 2-trees with n 3-gons. REFERENCES Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 327-328. F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 76, t(x), (3.5.19). LINKS T. Fowler, I. Gessel, G. Labelle, P. Leroux, The specification of 2-trees, Adv. Appl. Math. 28 (2) (2002) 145-168, Table 1. Andrew Gainer-Dewar, Gamma-Species and the Enumeration of k-Trees, Electronic Journal of Combinatorics, Volume 19 (2012), #P45. - From N. J. A. Sloane, Dec 15 2012 G. Labelle, C. Lamathe and P. Leroux, Labeled and unlabeled enumeration of k-gonal 2-trees, arXiv:math/0312424 [math.CO], 2003. EXAMPLE a(1)=a(2)=a(3)=1 because: K_2, K_3 are the only 2-trees on 2 and 3 nodes and on 4 nodes, there is a also unique example obtained by joining a triangle to K_3 along an edge (thus forming K_4\e). The two graphs on 5 nodes are obtained by joining a triangle to K_4\e, either along the shared edge or along one of the non-shared edges. CROSSREFS Cf. A036361. Cf. A000272 (labeled trees), A036361 (labeled 2-trees), A036362 (labeled 3-trees), A036506 (labeled 4-trees), A000055 (unlabeled trees). Sequence in context: A050237 A050258 A051436 * A203151 A140440 A005664 Adjacent sequences:  A054578 A054579 A054580 * A054582 A054583 A054584 KEYWORD nonn,nice AUTHOR Vladeta Jovovic, Apr 11 2000 EXTENSIONS Additional comments from Gordon F. Royle, Dec 02 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 5 12:04 EST 2020. Contains 338947 sequences. (Running on oeis4.)