A350823 Array read by antidiagonals: T(m,n) is the domination number of the grid graph P_m X P_n.

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

Author

Andrew Howroyd, Jan 17 2022

Keywords

• nonn
• tabl

Comments

Equivalently, the minimum number of X-pentominoes needed to cover an m X n grid.

Examples

			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 ...
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..276
• Eric Weisstein's World of Mathematics, Domination Number
• Eric Weisstein's World of Mathematics, Grid Graph

Crossrefs

Row 4 is A193768.

Main diagonal is A104519.

Cf. A286847, A300358, A350820.

Formula

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

T(1,n) = ceiling(n/3); T(2,n) = floor(n/2) + 1.