A303335 Array read by antidiagonals: T(m,n) is the number of minimum total dominating sets in the m X n king graph.

0, 1, 1, 2, 6, 2, 1, 9, 9, 1, 1, 4, 8, 4, 1, 4, 8, 1, 1, 8, 4, 3, 89, 3, 35, 3, 89, 3, 1, 56, 76, 9, 9, 76, 56, 1, 2, 16, 17, 1, 1, 1, 17, 16, 2, 9, 64, 1, 130, 9, 9, 130, 1, 64, 9, 4, 780, 6, 16, 60, 8684, 60, 16, 6, 780, 4, 1, 304, 229, 1, 89, 493, 493, 89, 1, 229, 304, 1

Offset

1,4

Comments

The minimum size of a total dominating set is the total domination number A303378(m, n).

Links

Andrew Howroyd, Table of n, a(n) for n = 1..435

Eric Weisstein's World of Mathematics, King Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

Example

Table begins:
=========================================
m\n| 1  2  3   4  5    6   7   8    9
---+-------------------------------------
1  | 0  1  2   1  1    4   3   1    2 ...
2  | 1  6  9   4  8   89  56  16   64 ...
3  | 2  9  8   1  3   76  17   1    6 ...
4  | 1  4  1  35  9    1 130  16    1 ...
5  | 1  8  3   9  1    9  60  89   45 ...
6  | 4 89 76   1  9 8684 493   1   50 ...
7  | 3 56 17 130 60  493 208  40   32 ...
8  | 1 16  1  16 89    1  40 604    1 ...
9  | 2 64  6   1 45   50  32   1 1192 ...
...

Crossrefs

Rows 1..2 are A302654, A350817.

Main diagonal is A303156.

Cf. A303114, A303293, A303378, A332390, A350815.

Sequence in context: A204935 A008905 A136760 * A332390 A289382 A062539

Adjacent sequences: A303332 A303333 A303334 * A303336 A303337 A303338

Keyword

nonn,tabl

Author

Andrew Howroyd, Apr 21 2018

Status

approved