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.

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, 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, 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

Offset: 1

Author

Brendan McKay

Keywords

• nonn
• tabf
• nice

Examples

			Triangle begins
  0;
  0,0;
  0,0,0,0;
  0,0,0,1,0,0,0;
  0,0,0,0,0,1,1,0,0,0;
  0,0,0,0,0,0,1,2,2,...;
  ...
From _Hugo Pfoertner_, Nov 24 2020: (Start)
Transposed table:
.
                              Nodes                        Sums
       4  5  6   7   8    9    10     11     12    13  14 |A002840
  Edges-+--+--+---+---+----+-----+------+------+-----+---+|-------
   6 | 1  .  .   .   .    .     .      .      .     .   . |      1
   7 | .  .  .   .   .    .     .      .      .     .   . |      0
   8 | .  1  .   .   .    .     .      .      .     .   . |      1
   9 | .  1  1   .   .    .     .      .      .     .   . |      2
  10 | .  .  2   .   .    .     .      .      .     .   . |      2
  11 | .  .  2   2   .    .     .      .      .     .   . |      4
  12 | .  .  2   8   2    .     .      .      .     .   . |     12
  13 | .  .  .  11  11    .     .      .      .     .   . |     22
  14 | .  .  .   8  42    8     .      .      .     .   . |     58
  15 | .  .  .   5  74   74     5      .      .     .   . |    158
  16 | .  .  .   .  76  296    76      .      .     .   . |    448
  17 | .  .  .   .  38  633   633     38      .     .   . |   1342
  18 | .  .  .   .  14  768  2635    768     14     .   . |   4199
  19 | .  .  .   .   .  538  6134   6134    558     .   . |  13384
  20 | .  .  .   .   .  219  8822  25626   8822   219   . |  43708
  21 | .  .  .   .   .   50  7916  64439  64439  7916  50 | 144810
  .. | .  .  .   .   .    .    ..     ..     ..    ..  .. |     ..
     ---+--+--+---+---+----+-----+------+-------+----+---+
  Sums 1  2  7  34 257 2606 32300 440564 6384634 .. A000944
(End)
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..469; rows 1..14 flattened

Crossrefs

Cf. A000944, A002840, A021103, A003094, A049334.

A049337, A058787, A212438 are all versions of the same triangle.

Cf. A058788.

Extensions

Missing zeros inserted by Sean A. Irvine, Jul 29 2021