A007021 Number of 4-connected simplicial polyhedra with n nodes. (Formerly M1214)

1, 1, 1, 1, 1, 2, 4, 10, 25, 87, 313, 1357, 6244, 30926, 158428, 836749, 4504607, 24649284, 136610879, 765598927, 4332047595, 24724362117, 142205424580, 823687567019, 4801749063379

Offset

3,6

Comments

Also the number of 4-connected triangulations on n vertices. - Manfred Scheucher, Mar 17 2023

References

M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties. Tech. Rep. 92-91, Info. and Comp. Sci. Dept., Univ. Calif. Irvine, 1992.

H. Heesch, Ein zum Vierfarbensatz aquivalenter Satz der Panisochromie [ A theorem of panisochromaticity equivalent to the four color theorem ], pp. 229-253 of Graph Theory in Memory of G. A. Dirac (Sandbjerg, 1985). Edited by L. D. Andersen et al., Annals of Discrete Mathematics, 41. North-Holland Publishing Co., Amsterdam-New York, 1989.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=3..27.

Gunnar Brinkmann and Brendan McKay, Guide to using plantri

Gunnar Brinkmann and Brendan McKay, Guide to using plantri [Cached copy, with permission]

S. Butler et al., Irreducible Apollonian configurations and packings, Discrete and Computational Geometry, 44 (2010), 487-507.

CombOS - Combinatorial Object Server, generate planar graphs

Paul Jungeblut, Edge Guarding Plane Graphs, Master Thesis, Karlsruhe Institute of Technology (Germany, 2019).

Irene Pivotto and Gordon Royle, Highly-connected planar cubic graphs with few or many Hamilton cycles, arXiv:1901.10683 [math.CO], 2019.

Manfred Scheucher, Hendrik Schrezenmaier, and Raphael Steiner, A Note On Universal Point Sets for Planar Graphs, arXiv:1811.06482 [math.CO], 2018.

Crossrefs

Cf. A000109, A007027, A111358.

Sequence in context: A085633 A111564 A350507 * A100605 A247395 A183947

Adjacent sequences: A007018 A007019 A007020 * A007022 A007023 A007024

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms generated with plantri by Moritz Firsching, Aug 20 2015

Status

approved