A377920 -id:A377920 - cp's OEIS frontend

A377921 Number of 3-connected Schnyder labelings with n inner faces in the quadrangular dissection, whose outer white vertices are non-isolated.

0, 0, 0, 1, 0, 3, 4, 15, 42, 131, 438, 1467, 5204, 18687, 69306, 261473, 1007328, 3943155, 15679474, 63199785, 257983836, 1065186381, 4444618518, 18725820855, 79603364236, 341206137453, 1473818915658, 6411853714819, 28082121491796, 123764682835371, 548675459164202

Offset: 0

N. J. A. Sloane, Dec 13 2024

nonn

Also number of strong equivalence classes of tricolored contact-systems with n+3 curves. - Éric Fusy, Dec 14 2024

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 s^tilde_n.

Cf. A377920, A377922, A377923, A342141.

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

A377922 Number of polyhedral orientations with n inner vertices.

Original entry on oeis.org

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

N. J. A. Sloane, Dec 13 2024

nonn

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

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.

Cf. A001181, A377920, A377921, A377923.

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

A377923 Number of corner polyhedra graphs of order n.

Original entry on oeis.org

0, 1, 0, 3, 4, 15, 39, 120

Offset: 0

N. J. A. Sloane, Dec 13 2024

Clément Dervieux, Dominique Poulalhon, and Gilles Schaeffer, The number of corner polyhedra graphs, Discrete Mathematics & Theoretical Computer Science (2020).

Cf. A377920, A377921, A377922.

cp's OEIS Frontend

A377921 Number of 3-connected Schnyder labelings with n inner faces in the quadrangular dissection, whose outer white vertices are non-isolated.

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A377922 Number of polyhedral orientations with n inner vertices.

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A377923 Number of corner polyhedra graphs of order n.

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