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

5,2

Links

Andrew Howroyd, Table of n, a(n) for n = 5..500

CombOS - Combinatorial Object Server, generate planar graphs

G. P. Michon, Counting Polyhedra

Example

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.

Prog

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

Crossrefs

Column k=4 of A342053.

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

Sequence in context: A179323 A001340 A275707 * A096654 A371312 A269509

Adjacent sequences: A058783 A058784 A058785 * A058787 A058788 A058789

Keyword

nonn,nice

Author

Gerard P. Michon, Nov 29 2000

Extensions

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

Status

approved