A377922 Number of polyhedral orientations with n inner vertices.

0, 0, 0, 1, 0, 3, 4, 15, 39, 122, 375, 1212, 3980, 13413, 45966, 160295, 566985, 2032110, 7368334, 27000759, 99891654, 372788553, 1402339329, 5313959388, 20272563265, 77822173758, 300473023929, 1166377045666, 4550358858954, 17835405078273, 70213720795466, 277552814035683

Offset

0,6

Comments

a(n) is also the number of combinatorial types of corner polyhedra with n+3 flats, and the number of weak equivalence classes of tricolored contact-systems with n+3 curves. - Éric Fusy, Dec 14 2024

Links

Table of n, a(n) for n=0..31.

Éric Fusy, E. Narmanli, and G. Schaeffer, Enumeration of corner polyhedra and 3-connected Schnyder labelings, arXiv preprint arXiv:2202.09172 [math.CO], 2022-2023. See p_n.

Crossrefs

Cf. A001181, A377920, A377921, A377923.

Sequence in context: A332051 A209479 A377923 * A209338 A377921 A127144

Adjacent sequences: A377919 A377920 A377921 * A377923 A377924 A377925

Keyword

nonn

Author

N. J. A. Sloane, Dec 13 2024

Extensions

a(13) onwards from Éric Fusy, Dec 14 2024

Status

approved