A350815 Array read by antidiagonals: T(m,n) is the number of minimum dominating sets in the m X n king graph.
1, 2, 2, 1, 4, 1, 4, 2, 2, 4, 3, 16, 1, 16, 3, 1, 12, 4, 4, 12, 1, 8, 4, 3, 256, 3, 4, 8, 4, 64, 1, 144, 144, 1, 64, 4, 1, 32, 8, 16, 79, 16, 8, 32, 1, 13, 8, 4, 4096, 9, 9, 4096, 4, 8, 13, 5, 208, 1, 1024, 1656, 1, 1656, 1024, 1, 208, 5, 1, 80, 13, 64, 408, 64, 64, 408, 64, 13, 80, 1
Offset: 1
Examples
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 ...
...
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
Crossrefs
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).
Comments