A263340 Triangle read by rows: T(n,k) is the number of graphs with n vertices containing k triangles.

1, 1, 2, 3, 1, 7, 2, 1, 0, 1, 14, 7, 5, 2, 3, 1, 0, 1, 0, 0, 1, 38, 23, 28, 14, 18, 9, 7, 5, 4, 1, 4, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 107, 102, 141, 117, 123, 92, 80, 63, 49, 35, 35, 23, 15, 17, 10, 4, 9, 5, 2, 3, 3, 2, 2, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1

Offset

0,3

Comments

Row sums give A000088.

First column is A006785.

Row lengths are 1 + binomial(n,3). - Geoffrey Critzer, Apr 13 2017

Links

Pontus von Brömssen, Rows n = 0..10, flattened

FindStat - Combinatorial Statistic Finder, The number of triangles of a graph.

Example

Triangle begins:
  1;
  1;
  2;
  3,1;
  7,2,1,0,1;
  14,7,5,2,3,1,0,1,0,0,1;
  38,23,28,14,18,9,7,5,4,1,4,1,1,1,0,0,1,0,0,0,1;
  ...

Mathematica

Table[Table[Count[Table[Tr[MatrixPower[AdjacencyMatrix[GraphData[{n, i}]], 3]]/6, {i, 1, NumberOfGraphs[n]}], k], {k, 0, Binomial[n, 3]}], {n, 1, 7}] (* Geoffrey Critzer, Apr 13 2017 *)

Crossrefs

Cf. A000088, A006785.

Sequence in context: A193491 A364271 A352062 * A114583 A114581 A328398

Adjacent sequences: A263337 A263338 A263339 * A263341 A263342 A263343

Keyword

nonn,tabf

Author

Christian Stump, Oct 15 2015

Extensions

Row 7 from Geoffrey Critzer, Apr 13 2017

T(0,0)=1 prepended by Alois P. Heinz, Apr 13 2017

Status

approved