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%I #2 Mar 30 2012 17:28:36
%S 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,
%T 14,768,2635,768,14,558,6134,6134,558,219,8822,25626,8822,219,50,7916,
%U 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
%N 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.
%C 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.
%H G. P. Michon, <a href="http://www.numericana.com/data/polyhedra.htm">Counting Polyhedra</a>
%e There are 768 different polyhedra with 18 edges and 9 or 11 faces.
%Y Cf. A000109, A002856, A000944, A002840, A058786, A058787, A049337, A008611.
%K nice,nonn,tabf
%O 6,5
%A _Gerard P. Michon_, Nov 29 2000
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