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

Author

Eunjeong Lee, Jun 29 2021

Keywords

• nonn

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

• 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.

Crossrefs

Cf. A003080.

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]).