A332404 Triangle read by rows: T(n,k) is the number of graphs on n unlabeled nodes with irredundance number k.

1, 1, 1, 2, 1, 1, 4, 5, 1, 1, 11, 16, 5, 1, 1, 34, 94, 21, 5, 1, 1, 156, 710, 150, 21, 5, 1, 1, 1044, 9419, 1691, 164, 21, 5, 1, 1, 12346, 221979, 38207, 1944, 164, 21, 5, 1, 1, 274668, 9907071, 1773452, 47802, 1983, 164, 21, 5, 1, 1

Offset

1,4

Comments

The irredundance number of a graph is the minimum size of a maximal irredundant set.

For any graph the following relation holds:

irredundance number (this sequence)

<= domination number (A263284)

<= independent domination number (A332402)

<= independence number (A263341)

<= upper domination number (A332403)

<= upper irredundance number (A332405).

Links

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

Eric Weisstein's World of Mathematics, Maximal Irredundant Set

Formula

T(n,k) = T(n-1,k-1) for 2*(k-1) >= n.

Example

Triangle begins:
       1;
       1,       1;
       2,       1,       1;
       4,       5,       1,     1;
      11,      16,       5,     1,    1;
      34,      94,      21,     5,    1,   1;
     156,     710,     150,    21,    5,   1,  1;
    1044,    9419,    1691,   164,   21,   5,  1, 1;
   12346,  221979,   38207,  1944,  164,  21,  5, 1, 1;
  274668, 9907071, 1773452, 47802, 1983, 164, 21, 5, 1, 1;
  ...

Crossrefs

Row sums are A000088.

Column k=1 is A000088(n-1).

Cf. A263284, A263341, A332402, A332403, A332404, A332405.

Sequence in context: A294206 A332402 A263284 * A308905 A158471 A158472

Adjacent sequences: A332401 A332402 A332403 * A332405 A332406 A332407

Keyword

nonn,tabl

Author

Andrew Howroyd, Feb 11 2020

Status

approved