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A350823
Array read by antidiagonals: T(m,n) is the domination number of the grid graph P_m X P_n.
4
1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 3, 3, 2, 2, 3, 4, 4, 3, 2, 3, 4, 4, 4, 4, 4, 3, 3, 4, 5, 6, 6, 5, 4, 3, 3, 5, 6, 7, 7, 7, 6, 5, 3, 4, 5, 7, 7, 8, 8, 7, 7, 5, 4, 4, 6, 7, 8, 9, 10, 9, 8, 7, 6, 4, 4, 6, 8, 10, 11, 11, 11, 11, 10, 8, 6, 4
OFFSET
1,5
COMMENTS
Equivalently, the minimum number of X-pentominoes needed to cover an m X n grid.
LINKS
Eric Weisstein's World of Mathematics, Domination Number
Eric Weisstein's World of Mathematics, Grid Graph
FORMULA
T(m,n) = T(n,m).
T(1,n) = ceiling(n/3); T(2,n) = floor(n/2) + 1.
EXAMPLE
Table begins:
===================================
m\n | 1 2 3 4 5 6 7 8 9
----+------------------------------
1 | 1 1 1 2 2 2 3 3 3 ...
2 | 1 2 2 3 3 4 4 5 5 ...
3 | 1 2 3 4 4 5 6 7 7 ...
4 | 2 3 4 4 6 7 7 8 10 ...
5 | 2 3 4 6 7 8 9 11 12 ...
6 | 2 4 5 7 8 10 11 12 14 ...
7 | 3 4 6 7 9 11 12 14 16 ...
8 | 3 5 7 8 11 12 14 16 18 ...
9 | 3 5 7 10 12 14 16 18 20 ...
...
CROSSREFS
Row 4 is A193768.
Main diagonal is A104519.
Sequence in context: A230198 A024939 A024937 * A143977 A115265 A105223
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Jan 17 2022
STATUS
approved