A303118 Array read by antidiagonals: T(m,n) = number of minimal total dominating sets in the grid graph P_m X P_n.

0, 1, 1, 2, 4, 2, 1, 4, 4, 1, 2, 16, 6, 16, 2, 4, 16, 49, 49, 16, 4, 3, 49, 66, 169, 66, 49, 3, 4, 81, 225, 576, 576, 225, 81, 4, 8, 169, 640, 2601, 2622, 2601, 640, 169, 8, 9, 324, 1681, 10000, 14400, 14400, 10000, 1681, 324, 9, 10, 625, 4641, 38416, 81055, 137641, 81055, 38416, 4641, 625, 10

Offset

1,4

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
---+---------------------------------------------------------
1  | 0   1    2     1      2       4         3          4 ...
2  | 1   4    4    16     16      49        81        169 ...
3  | 2   4    6    49     66     225       640       1681 ...
4  | 1  16   49   169    576    2601     10000      38416 ...
5  | 2  16   66   576   2622   14400     81055     440896 ...
6  | 4  49  225  2601  14400  137641   1081600    8185321 ...
7  | 3  81  640 10000  81055 1081600  11458758  125955729 ...
8  | 4 169 1681 38416 440896 8185321 125955729 1944369025 ...
...

Crossrefs

Rows 1..2 are A302655, A303072.

Main diagonal is A303161.

Cf. A300358, A303111, A303293.

Sequence in context: A364608 A105791 A116515 * A037178 A352650 A364038

Adjacent sequences: A303115 A303116 A303117 * A303119 A303120 A303121

Keyword

nonn,tabl

Author

Andrew Howroyd, Apr 18 2018

Status

approved