A324244 Triangle read by rows: T(n,k) is the number of connected graphs on n nodes with k peripheral nodes.

1, 0, 1, 0, 1, 1, 0, 2, 2, 2, 0, 5, 4, 7, 5, 0, 25, 20, 16, 23, 28, 0, 185, 146, 119, 57, 123, 223, 0, 2459, 1728, 1523, 948, 405, 903, 3151, 0, 58156, 36109, 32119, 24637, 13927, 4713, 11746, 79673, 0, 2617378, 1446609, 1304109, 1026845, 723871, 353620, 110734, 279535, 3853870

Offset

1,8

Comments

The peripheral nodes of a graph are those with eccentricity equal to the diameter.

Links

Table of n, a(n) for n=1..55.

Eric Weisstein's World of Mathematics, Graph Periphery

Wikipedia, Distance (graph theory)

Example

Triangle begins:
  1;
  0,     1;
  0,     1,     1;
  0,     2,     2,     2;
  0,     5,     4,     7,     5;
  0,    25,    20,    16,    23,    28;
  0,   185,   146,   119,    57,   123,  223;
  0,  2459,  1728,  1523,   948,   405,  903,  3151;
  0, 58156, 36109, 32119, 24637, 13927, 4713, 11746, 79673;
  ...

Crossrefs

Row sums give A001349.

Column k=2 is A324263.

Rightmost diagonal is A324264.

Cf. A294522, A294525, A324239.

Sequence in context: A084203 A073358 A124342 * A082835 A104241 A011139

Adjacent sequences: A324241 A324242 A324243 * A324245 A324246 A324247

Keyword

nonn,tabl

Author

Andrew Howroyd, Sep 02 2019

Status

approved