OFFSET
1,2
COMMENTS
The minimum size of a dominating set is the domination number which in the case of an m X n king graph is given by (ceiling(m/3) * ceiling(n/3)).
LINKS
Stephan Mertens, Table of n, a(n) for n = 1..946 (first 276 terms from Andrew Howroyd)
Stephan Mertens, Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph, arXiv:2408.08053 [math.CO], Aug 2024.
Eric Weisstein's World of Mathematics, King Graph
Eric Weisstein's World of Mathematics, Minimum Dominating Set
FORMULA
T(n,m) = T(m,n).
T(3*m, 3*n) = 1; T(3*m+1, 3*n) = (m^2 + 5*m + 2)^n; T(3*m+2, 3*n) = (m+2)^n.
T(3*m-1, 3*n-1) = A350819(m, n).
EXAMPLE
Table begins:
============================================
m\n | 1 2 3 4 5 6 7 8
----+---------------------------------------
1 | 1 2 1 4 3 1 8 4 ...
2 | 2 4 2 16 12 4 64 32 ...
3 | 1 2 1 4 3 1 8 4 ...
4 | 4 16 4 256 144 16 4096 1024 ...
5 | 3 12 3 144 79 9 1656 408 ...
6 | 1 4 1 16 9 1 64 16 ...
7 | 8 64 8 4096 1656 64 243856 29744 ...
8 | 4 32 4 1024 408 16 29744 3600 ...
...
CROSSREFS
AUTHOR
Andrew Howroyd, Jan 17 2022
STATUS
approved