A058787 - OEIS

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A058787

Triangle T(n,k) = number of polyhedra (triconnected planar graphs) with n faces and k vertices, where (n/2+2) <= k <= (2n+8).

1, 1, 1, 1, 2, 2, 2, 2, 8, 11, 8, 5, 2, 11, 42, 74, 76, 38, 14, 8, 74, 296, 633, 768, 558, 219, 50, 5, 76, 633, 2635, 6134, 8822, 7916, 4442, 1404, 233, 38, 768, 6134, 25626, 64439, 104213, 112082, 79773, 36528, 9714, 1249, 14, 558, 8822, 64439, 268394, 709302

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OFFSET

4,5

COMMENTS

Rows are of lengths 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, ... floor(3n/2)-5. See A001651 (this is the sequence of integers not divisible by 3).

LINKS

Table of n, a(n) for n=4..57.

G. P. Michon, Counting Polyhedra

EXAMPLE

There are 38 polyhedra with 9 faces and 11 vertices, or with 11 faces and 9 vertices.

CROSSREFS

Cf. A000109, A002856, A000944, A002840, A058786, A058788, A001651.