A362868 Triangle read by rows: T(n,k) is the number of connected simple graphs G of order n with the property that k is the order of the largest quotient graph G/~ that is a complete graph. 1 <= k <= n.

1, 0, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 12, 7, 1, 0, 1, 23, 75, 12, 1, 0, 1, 24, 481, 329, 17, 1

Offset

1,9

Comments

Row sums are given by A001349.

T(n,2) = 1 is the star graph of order n for n >= 2.

T(n,n) = 1 is the complete graph of order n.

Links

Table of n, a(n) for n=1..28.

FindStat, St001670: The connected partition number of a graph.

Example

n\k | 1  2   3    4    5   6  7
----+------------------------------
  1 | 1,
  2 | 0, 1
  3 | 0, 1,  1
  4 | 0, 1,  4,   1
  5 | 0, 1, 12,   7,   1
  6 | 0, 1, 23,  75,  12,  1
  7 | 0, 1, 24, 481, 329, 17, 1

Crossrefs

Cf. A001349 (row sums).

Sequence in context: A123125 A173018 A369971 * A055105 A348600 A200545

Adjacent sequences: A362865 A362866 A362867 * A362869 A362870 A362871

Keyword

nonn,tabl,hard,more

Author

Peter Kagey, May 06 2023

Status

approved