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

1,6

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.

Prog

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

Crossrefs

Row sums of A380361.

Antidiagonal sums of A295633.

Cf. A005043, A346779, A380362.

Sequence in context: A153967 A052949 A014266 * A032441 A238184 A340333

Adjacent sequences: A380355 A380356 A380357 * A380361 A380362 A380363

Keyword

nonn,new

Author

Andrew Howroyd, Jan 25 2025

Status

approved