A367145 Triangle read by rows: T(n,k) is the number of simple graphs on n unlabeled nodes with k simplical vertices, 0 <= k <= n.

1, 0, 1, 0, 0, 2, 0, 0, 1, 3, 1, 0, 2, 3, 5, 4, 3, 4, 8, 8, 7, 24, 24, 25, 26, 29, 17, 11, 191, 239, 205, 153, 126, 80, 35, 15, 3095, 3475, 2617, 1491, 893, 480, 208, 65, 22, 95208, 87636, 51224, 23800, 10189, 4351, 1627, 485, 118, 30, 5561999, 3863137, 1691007, 604999, 196486, 62180, 19084, 4949, 1082, 203, 42

Offset

0,6

Comments

A simplical vertex is one whose neighbors induce a complete graph.

Links

Table of n, a(n) for n=0..65.

Wikipedia, Vertex_(graph_theory).

Example

Triangle begins:
    1;
    0,   1;
    0,   0,   2;
    0,   0,   1,   3;
    1,   0,   2,   3,   5;
    4,   3,   4,   8,   8,  7;
   24,  24,  25,  26,  29, 17, 11;
  191, 239, 205, 153, 126, 80, 35, 15;
  ...

Crossrefs

Column k=0 is A367144.

Row sums are A000088.

Main diagonal is A000041.

Sequence in context: A291170 A275001 A290975 * A291678 A286180 A291701

Adjacent sequences: A367142 A367143 A367144 * A367146 A367147 A367148

Keyword

nonn,tabl

Author

Andrew Howroyd, Nov 06 2023

Status

approved