A212438 Irregular triangle read by rows: T(n,k) is the number of polyhedra with n faces and k vertices (n >= 4, k=4..2n-4).

1, 0, 1, 1, 0, 1, 2, 2, 2, 0, 0, 2, 8, 11, 8, 5, 0, 0, 2, 11, 42, 74, 76, 38, 14, 0, 0, 0, 8, 74, 296, 633, 768, 558, 219, 50, 0, 0, 0, 5, 76, 633, 2635, 6134, 8822, 7916, 4442, 1404, 233, 0, 0, 0, 0, 38, 768, 6134, 25626, 64439, 104213, 112082, 79773, 36528, 9714, 1249

Offset

4,7

Comments

Because of duality, T(n,k) = T(k,n). - Ivan Neretin, May 25 2016

The number of edges is n+k-2. - Andrew Howroyd, Mar 27 2021

Links

Andrew Howroyd, Table of n, a(n) for n = 4..199 (rows 4..17)

Gunnar Brinkmann and Brendan McKay, Fast generation of planar graphs (expanded edition), Table 9-11.

G. P. Michon, Counting Polyhedra

Example

Triangle begins:
1
0 1 1
0 1 2  2  2
0 0 2  8 11   8    5
0 0 2 11 42  74   76   38   14
0 0 0  8 74 296  633  768  558  219   50
0 0 0  5 76 633 2635 6134 8822 7916 4442 1404 233
...

Crossrefs

A049337, A058787, A212438 are all versions of the same triangle.

Row sums (the same as column sums) are A000944.

Main diagonal is A002856.

Cf. A002840 (by edges), A239893.

Sequence in context: A181676 A262048 A034852 * A112790 A329922 A179835

Adjacent sequences: A212435 A212436 A212437 * A212439 A212440 A212441

Keyword

nonn,tabf

Author

N. J. A. Sloane, May 16 2012

Extensions

Terms a(53) and beyond from Andrew Howroyd, Mar 27 2021

Status

approved