A345955 Number of isomorphism classes of indecomposable Fano Bott manifolds of complex dimension n.

1, 1, 3, 7, 21, 60, 189, 595, 1948, 6455, 21804, 74464, 257311, 896874, 3151564, 11148982, 39680010, 141969156, 510352307, 1842370850, 6676349598, 24277171876, 88556616799, 323959047186, 1188237214539, 4368874535437, 16099389598907, 59449932709972, 219953954227839

Offset

1,3

Comments

a(n) is also the number of rooted triangular cacti with 2n+1 nodes (n triangles) with one triangle at the root vertex.

Links

Table of n, a(n) for n=1..29.

Yunhyung Cho, Eunjeong Lee, Mikiya Masuda, and Seonjeong Park, On the enumeration of Fano Bott manifolds, arXiv:2106.12788 [math.AG], 2021. See Table 1 p. 8.

Frank Harary and George E. Uhlenbeck, On the number of Husimi trees. I, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 315-322.

Formula

G.f.: (x/2)*(F(x^2)+F(x)^2) where F(x) is the g.f. of A003080 (see the equation (1) in [Harary-Uhlenbeck] or [Cho-Lee-Masuda-Park, Lemma 4.3]).

Crossrefs

Cf. A003080.

Sequence in context: A182887 A035080 A229188 * A091486 A056779 A183113

Adjacent sequences: A345952 A345953 A345954 * A345956 A345957 A345958

Keyword

nonn

Author

Eunjeong Lee, Jun 29 2021

Status

approved