A350819 Array read by antidiagonals: T(m,n) is the number of maximum independent sets in the 2m X 2n king graph.

1, 1, 1, 1, 4, 1, 1, 12, 12, 1, 1, 32, 79, 32, 1, 1, 80, 408, 408, 80, 1, 1, 192, 1847, 3600, 1847, 192, 1, 1, 448, 7698, 26040, 26040, 7698, 448, 1, 1, 1024, 30319, 166368, 281571, 166368, 30319, 1024, 1, 1, 2304, 114606, 976640, 2580754, 2580754, 976640, 114606, 2304, 1

Offset: 0

Author

Andrew Howroyd, Jan 17 2022

Keywords

• nonn
• tabl

Comments

Number of ways to tile a (2m+1) X (2n+1) board with m*n 2 X 2 tiles and 2m+2n+1 1 X 1 tiles.

For m,n > 0, T(m,n) is the number of minimum dominating sets in the (3m-1) X (3n-1) king graph.

Examples

			Table begins:
=============================================
m\n | 0   1    2      3       4        5
----+----------------------------------------
  0 | 1   1    1      1       1        1 ...
  1 | 1   4   12     32      80      192 ...
  2 | 1  12   79    408    1847     7698 ...
  3 | 1  32  408   3600   26040   166368 ...
  4 | 1  80 1847  26040  281571  2580754 ...
  5 | 1 192 7698 166368 2580754 32572756 ...
  ...
		

Links

• Eric Weisstein's World of Mathematics, King Graph
• Eric Weisstein's World of Mathematics, Maximum Independent Vertex Set

Crossrefs

Rows 0..12 are A000012, A001787(n+1), A061593, A061594, A173782, A173783, A174154, A174155, A174558, A195648, A195649, A195650, A195651.

Main diagonal is A018807.

Cf. A350815, A350818.

Formula

T(m,n) = T(n,m).

T(m,n) = A350818(2*m, 2*n) = A350815(3*m-1, 3*n-1).