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A049337 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.

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