A300358 Array read by antidiagonals: T(m,n) = total domination number of the grid graph P_m X P_n.
1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 5, 4, 4, 4, 6, 6, 8, 8, 6, 6, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 6, 6, 8, 10, 10, 10, 10, 8, 6, 6, 6, 8, 9, 12, 12, 12, 12, 12, 9, 8, 6, 6, 8, 10, 12, 14, 14, 14, 14, 12, 10, 8, 6, 7, 8, 11, 14, 15, 16, 15, 16, 15, 14, 11, 8, 7
Offset: 1
Examples
Table begins: ======================================================= m\n| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ---+--------------------------------------------------- 1 | 1 2 2 2 3 4 4 4 5 6 6 6 7 8 8 8 ... 2 | 2 2 2 4 4 4 6 6 6 8 8 8 10 10 10 12 ... 3 | 2 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ... 4 | 2 4 4 6 8 8 10 12 12 14 14 16 18 18 20 20 ... 5 | 3 4 5 8 9 10 12 14 15 16 18 20 21 22 24 26 ... 6 | 4 4 6 8 10 12 14 16 18 20 20 24 24 26 28 30 ... 7 | 4 6 7 10 12 14 15 18 20 22 24 26 27 30 32 34 ... 8 | 4 6 8 12 14 16 18 20 22 24 28 30 32 34 36 38 ... 9 | 5 6 9 12 15 18 20 22 25 28 30 32 35 38 40 42 ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..435 (first 29 antidiagonals)
- Alexandre Talon, Intensive use of computing resources for dominations in grids and other combinatorial problems, arXiv:2002.11615 [cs.DM], 2020. See Sec. 2.3.2.
- Eric Weisstein's World of Mathematics, Grid Graph
- Eric Weisstein's World of Mathematics, Total Domination Number