A058788 Triangle T(n,k) = number of polyhedra (triconnected planar graphs) with n edges and k vertices (or k faces), where (n/3+2) <= k <= (2n/3). Note that there is no such k when n=7.

1, 1, 1, 1, 2, 2, 2, 2, 8, 2, 11, 11, 8, 42, 8, 5, 74, 74, 5, 76, 296, 76, 38, 633, 633, 38, 14, 768, 2635, 768, 14, 558, 6134, 6134, 558, 219, 8822, 25626, 8822, 219, 50, 7916, 64439, 64439, 7916, 50, 4442, 104213, 268394, 104213, 4442, 1404, 112082, 709302, 709302, 112082, 1404, 233, 79773, 1263032, 2937495, 1263032, 79773, 233, 36528, 1556952, 8085725, 8085725, 1556952, 36528, 9714, 1338853, 15535572, 33310550

Offset

6,5

Comments

Rows are of lengths 1,0,1,2,1,2,3,2,3,4,3,4,5,4,5,6,5, ... n-1-2*floor((n+2)/3). See A008611. Note the zero length, which means that there are no polyhedra with n=7 edges.

Links

Table of n, a(n) for n=6..79.

G. P. Michon, Counting Polyhedra

Example

There are 768 different polyhedra with 18 edges and 9 or 11 faces.

Crossrefs

Cf. A000109, A002856, A000944, A002840, A058786, A058787, A049337, A008611.

Sequence in context: A168281 A203610 A294873 * A013598 A100943 A152660

Adjacent sequences: A058785 A058786 A058787 * A058789 A058790 A058791

Keyword

nice,nonn,tabf

Author

Gerard P. Michon, Nov 29 2000

Status

approved