%I
%S 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,
%T 219,50,5,76,633,2635,6134,8822,7916,4442,1404,233,38,768,6134,25626,
%U 64439,104213,112082,79773,36528,9714,1249,14,558,8822,64439,268394,709302
%N Triangle T(n,k) = number of polyhedra (triconnected planar graphs) with n faces and k vertices, where (n/2+2) <= k <= (2n+8).
%C 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).
%H G. P. Michon, <a href="http://www.numericana.com/data/polyhedra.htm">Counting Polyhedra</a>
%e There are 38 polyhedra with 9 faces and 11 vertices, or with 11 faces and 9 vertices.
%Y Cf. A000109, A002856, A000944, A002840, A058786, A058788, A001651.
%Y A049337, A058787, A212438 are all versions of the same triangle.
%K hard,nice,nonn,tabf
%O 4,5
%A _Gerard P. Michon_, Nov 29 2000
