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A300358
Array read by antidiagonals: T(m,n) = total domination number of the grid graph P_m X P_n.
6
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
1,2
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
EXAMPLE
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 ...
...
CROSSREFS
Rows 1..2 are A004524(n+2), A302402.
Main diagonal is A302488.
Sequence in context: A167383 A167661 A187187 * A102682 A116371 A103377
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Apr 20 2018
STATUS
approved