A380360 Number of embeddings on the sphere of Halin graphs on n unlabeled nodes up to orientation-preserving homeomorphisms.

0, 0, 0, 1, 1, 2, 2, 4, 7, 16, 32, 76, 181, 443, 1098, 2793, 7127, 18458, 48128, 126580, 334955, 892187, 2388674, 6428489, 17377599, 47174939, 128555088, 351580903, 964696719, 2655197386, 7329051870, 20284610084, 56283140111, 156537249660, 436338547904, 1218824493990, 3411297202411

Offset: 1

Author

Andrew Howroyd, Jan 25 2025

Keywords

• nonn

Comments

Halin graphs are planar and 3-connected and can be embedding in the sphere in essentially one way up to mirror symmetry. This sequence counts each graph as either 1 or 2 depending on if it is mirror symmetric.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Halin Graph.
• Wikipedia, Halin graph.

Crossrefs

Row sums of A380361.

Antidiagonal sums of A295633.

Cf. A005043, A346779, A380362.

Programs

PARI

A380360seq(36) \\ See PARI Link in A380362 for program code.