A058786 Number of n-hedra with 2n-5 vertices or 3n-7 edges (the vertices of these are all of degree 3, except one which is of degree 4). Alternatively, the number of polyhedra with n vertices whose faces are all triangular, except one which is tetragonal.

1, 2, 8, 38, 219, 1404, 9714, 70454, 527235, 4037671, 31477887, 249026400, 1994599707, 16147744792, 131959532817, 1087376999834, 9027039627035, 75441790558926, 634311771606750, 5362639252793358, 45565021714371644, 388937603694422120, 3333984869758146814

Offset: 5

Author

Gerard P. Michon, Nov 29 2000

Keywords

• nonn
• nice

Examples

			a(5)=1 because the square pyramid is the only pentahedron with 5=2*5-5 vertices (or 8=3*5-7 edges). Alternatively, a(5)=1 because the square pyramid is the only polyhedron with 5 vertices whose faces are all triangles with only one tetragonal exception.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 5..500
• CombOS - Combinatorial Object Server, generate planar graphs
• G. P. Michon, Counting Polyhedra

Crossrefs

Column k=4 of A342053.

Cf. A000109, A002856, A000944, A002840, A058787, A058788, A049337.

Programs

PARI

A342053ColSeq(25,4) \\ See links in A342053. - Andrew Howroyd, Feb 28 2021

Extensions

Terms a(19) and beyond from Andrew Howroyd, Feb 27 2021