A303293 Array read by antidiagonals: T(m,n) = number of minimum total dominating sets in the grid graph P_m X P_n.

0, 1, 1, 2, 4, 2, 1, 1, 1, 1, 1, 16, 2, 16, 1, 4, 9, 1, 1, 9, 4, 3, 1, 3, 16, 3, 1, 3, 1, 64, 4, 256, 256, 4, 64, 1, 2, 16, 4, 4, 160, 4, 4, 16, 2, 9, 1, 9, 121, 25, 25, 121, 9, 1, 9, 4, 169, 12, 2916, 268, 144, 268, 2916, 12, 169, 4

Offset

1,4

Comments

The minimum size of a total dominating set is the total domination number A300358(m, n).

Links

Andrew Howroyd, Table of n, a(n) for n = 1..435 (first 29 antidiagonals)

Eric Weisstein's World of Mathematics, Grid 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  4  1   16    9     1  64   16     1 ...
3  | 2  1  2    1    3     4   4    9    12 ...
4  | 1 16  1   16  256     4 121 2916    25 ...
5  | 1  9  3  256  160    25 268 4225   510 ...
6  | 4  1  4    4   25   144 529 2025 10404 ...
7  | 3 64  4  121  268   529   4  441   630 ...
8  | 1 16  9 2916 4225  2025 441  256     9 ...
9  | 2  1 12   25  510 10404 630    9  1364 ...
...

Crossrefs

Rows 1..2 are A302654, A303054.

Main diagonal is A303142.

Cf. A300358, A303111, A303118.

Sequence in context: A201316 A105023 A279315 * A344637 A201558 A052285

Adjacent sequences: A303290 A303291 A303292 * A303294 A303295 A303296

Keyword

nonn,tabl

Author

Andrew Howroyd, Apr 20 2018

Status

approved