A123545 Triangle read by rows: T(n,k) = number of unlabeled connected graphs on n nodes with degree >= 3 at each node (n >= 1, 0 <= k <= n(n-1)/2).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 5, 4, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 18, 30, 34, 29, 17, 9, 5, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 35, 136, 309, 465, 505, 438, 310, 188, 103, 52, 23

Offset

1,35

References

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.

Links

R. W. Robinson, Rows 1 through 14, flattened

Example

Triangle begins:
n = 1
k = 0 : 0
************************ TOTAL (n = 1) = 0
n = 2
k = 0 : 0
k = 1 : 0
************************ TOTAL (n = 2) = 0
n = 3
k = 0 : 0
k = 1 : 0
k = 2 : 0
k = 3 : 0
************************ TOTAL (n = 3) = 0
n = 4
k = 0 : 0
k = 1 : 0
k = 2 : 0
k = 3 : 0
k = 4 : 0
k = 5 : 0
k = 6 : 1
************************ TOTAL (n = 4) = 1
n = 5
k = 0 : 0
k = 1 : 0
k = 2 : 0
k = 3 : 0
k = 4 : 0
k = 5 : 0
k = 6 : 0
k = 7 : 0
k = 8 : 1
k = 9 : 1
k = 10 : 1
************************ TOTAL (n = 5) = 3
From Hugo Pfoertner, Nov 22 2020: (Start)
Transposed table:
                            Nodes                             Sums
       4  5  6   7    8      9      10      11     12    13 |A338604
  Edges-----------------------------------------------------|-------
   6 | 1  .  .   .    .      .       .       .      .     . |      1
   7 | .  .  .   .    .      .       .       .      .     . |      0
   8 | .  1  .   .    .      .       .       .      .     . |      1
   9 | .  1  2   .    .      .       .       .      .     . |      3
  10 | .  1  4   .    .      .       .       .      .     . |      5
  11 | .  .  5   4    .      .       .       .      .     . |      9
  12 | .  .  4  18    5      .       .       .      .     . |     27
  13 | .  .  2  30   35      .       .       .      .     . |     67
  14 | .  .  1  34  136     27       .       .      .     . |    198
  15 | .  .  1  29  309    288      19       .      .     . |    646
  16 | .  .  .  17  465   1377     357       .      .     . |   2216
  17 | .  .  .   9  505   3978    3478     208      .     . |   8178
  18 | .  .  .   5  438   7956   18653    4958     85     . |  32085
  19 | .  .  .   2  310  11904   65011   50575   4291     . | 132093
  20 | .  .  .   1  188  14134  163812  302854  85421  1958 | 568368
(End)

Crossrefs

Row sums give A007112. Cf. A123546, A338604.

Sequence in context: A358339 A230564 A011174 * A123546 A339069 A372983

Adjacent sequences: A123542 A123543 A123544 * A123546 A123547 A123548

Keyword

nonn,tabf

Author

N. J. A. Sloane, Nov 13 2006

Status

approved