A303378 Array read by antidiagonals: T(m,n) = total domination number of the m X n king graph.

1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 4, 3, 2, 2, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 6, 5, 4, 6, 6, 6, 6, 4, 5, 6, 6, 6, 5, 6, 7, 8, 7, 6, 5, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 6, 6, 6, 6, 7, 6, 6, 8, 9, 8, 9, 8, 9, 8, 6, 6, 7

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..496

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 10 11 12 13 14 15 16
---+---------------------------------------------------
1  | 1  2  2  2  3  4  4  4  5  6  6  6  7  8  8  8 ...
2  | 2  2  2  2  3  4  4  4  5  6  6  6  7  8  8  8 ...
3  | 2  2  2  2  3  4  4  4  5  6  6  6  7  8  8  8 ...
4  | 2  2  2  4  4  4  6  6  6  8  8  8 10 10 10 12 ...
5  | 3  3  3  4  5  6  7  8  9 10 11 12 13 14 15 16 ...
6  | 4  4  4  4  6  8  8  8 10 12 12 12 14 16 16 16 ...
7  | 4  4  4  6  7  8  9 10 11 12 14 14 16 17 18 19 ...
8  | 4  4  4  6  8  8 10 12 12 14 16 16 18 20 20 22 ...
9  | 5  5  5  6  9 10 11 12 15 16 17 18 21 22 23 24 ...
...

Crossrefs

Main diagonal is A302401.

Cf. A300358, A303114, A303335.

Sequence in context: A104230 A226774 A037968 * A074908 A307713 A328680

Adjacent sequences: A303375 A303376 A303377 * A303379 A303380 A303381

Keyword

nonn,tabl

Author

Andrew Howroyd, Apr 22 2018

Status

approved