A332405 Triangle read by rows: T(n,k) is the number of simple graphs on n unlabeled nodes with upper irredundance number k.

1, 1, 1, 1, 2, 1, 1, 6, 3, 1, 1, 13, 15, 4, 1, 1, 36, 83, 30, 5, 1, 1, 101, 582, 302, 51, 6, 1, 1, 364, 6025, 5025, 843, 80, 7, 1, 1, 1511, 99503, 144371, 27160, 1996, 117, 8, 1, 1, 7917, 2706030, 7441332, 1733212, 112291, 4211, 164, 9, 1

Offset: 1

Author

Andrew Howroyd, Feb 11 2020

Keywords

• nonn
• tabl

Comments

First differs from A332403 in row 7.

The upper irredundance number of a graph is the maximum size of an irredundant set. For any graph the upper irredundance number is greater than or equal to the upper domination number (A332403).

Examples

			Triangle begins:
  1;
  1,    1;
  1,    2,       1;
  1,    6,       3,       1;
  1,   13,      15,       4,       1;
  1,   36,      83,      30,       5,      1;
  1,  101,     582,     302,      51,      6,    1;
  1,  364,    6025,    5025,     843,     80,    7,   1;
  1, 1511,   99503,  144371,   27160,   1996,  117,   8, 1;
  1, 7917, 2706030, 7441332, 1733212, 112291, 4211, 164, 9, 1;
  ...
		

Links

• Eric Weisstein's World of Mathematics, Irredundant Set

Crossrefs

Row sums are A000088.

Cf. A263284, A263341, A332402, A332403, A332404.