%I #20 Jul 30 2021 08:34:08
%S 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,2,2,
%T 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,8,11,8,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,2,11,42,74,76,38,14,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,74,296,633,768,558,219,50
%N Triangle read by rows: T(n,k) is the number of 3-connected planar graphs (or polyhedra) with n >= 1 nodes and 0 <= k <= C(n,2) edges.
%H Sean A. Irvine, <a href="/A049337/b049337.txt">Table of n, a(n) for n = 1..469; rows 1..14 flattened</a>
%e Triangle begins
%e 0;
%e 0,0;
%e 0,0,0,0;
%e 0,0,0,1,0,0,0;
%e 0,0,0,0,0,1,1,0,0,0;
%e 0,0,0,0,0,0,1,2,2,...;
%e ...
%e From _Hugo Pfoertner_, Nov 24 2020: (Start)
%e Transposed table:
%e .
%e Nodes Sums
%e 4 5 6 7 8 9 10 11 12 13 14 |A002840
%e Edges-+--+--+---+---+----+-----+------+------+-----+---+|-------
%e 6 | 1 . . . . . . . . . . | 1
%e 7 | . . . . . . . . . . . | 0
%e 8 | . 1 . . . . . . . . . | 1
%e 9 | . 1 1 . . . . . . . . | 2
%e 10 | . . 2 . . . . . . . . | 2
%e 11 | . . 2 2 . . . . . . . | 4
%e 12 | . . 2 8 2 . . . . . . | 12
%e 13 | . . . 11 11 . . . . . . | 22
%e 14 | . . . 8 42 8 . . . . . | 58
%e 15 | . . . 5 74 74 5 . . . . | 158
%e 16 | . . . . 76 296 76 . . . . | 448
%e 17 | . . . . 38 633 633 38 . . . | 1342
%e 18 | . . . . 14 768 2635 768 14 . . | 4199
%e 19 | . . . . . 538 6134 6134 558 . . | 13384
%e 20 | . . . . . 219 8822 25626 8822 219 . | 43708
%e 21 | . . . . . 50 7916 64439 64439 7916 50 | 144810
%e .. | . . . . . . .. .. .. .. .. | ..
%e ---+--+--+---+---+----+-----+------+-------+----+---+
%e Sums 1 2 7 34 257 2606 32300 440564 6384634 .. A000944
%e (End)
%Y Cf. A000944, A002840, A021103, A003094, A049334.
%Y A049337, A058787, A212438 are all versions of the same triangle.
%Y Cf. A058788.
%K nonn,tabf,nice
%O 1,33
%A _Brendan McKay_
%E Missing zeros inserted by _Sean A. Irvine_, Jul 29 2021