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A279408 Triangle read by rows: T(n,m) (n>=m>=1) = domination number for kings' graph on an n X m toroidal board.

%I A279408 #21 Mar 09 2017 10:01:09
%S A279408 1,1,1,1,1,1,2,2,2,3,2,2,2,4,4,2,2,2,4,4,4,3,3,3,5,5,6,7,3,3,3,6,6,6,
%T A279408 8,8,3,3,3,6,6,6,9,9,9,4,4,4,7,7,8,10,11,12,14,4,4,4,8,8,8,11,11,12,
%U A279408 15,15,4,4,4,8,8,8,12,12,12,16,16,16,5,5,5,9,9,10,13,14,15,18,19,20,22
%N A279408 Triangle read by rows: T(n,m) (n>=m>=1) = domination number for kings' graph on an n X m toroidal board.
%C A279408 That is, the minimal number of kings needed to cover an n X m toroidal chessboard so that every square has a king on it, is under attack by a king, or both.
%C A279408 For the usual non-toroidal case, the formula is ceiling(m/3)*ceiling(n/3).
%D A279408 John J. Watkins, Across the Board: The Mathematics of Chessboard Problem, Princeton University Press, 2004, pages 144-149.
%H A279408 Indranil Ghosh, <a href="/A279408/b279408.txt">Rows 1..100, flattened</a>
%H A279408 Dan Freeman, <a href="http://www.slideshare.net/DanFreeman1/chessboard-puzzles-part-4-other-surfaces-and-variations-42702023">Chessboard Puzzles Part 4 - Other Surfaces and Variations</a>.
%F A279408 T(n,m) = ceiling(max(m*ceiling(n/3), n*ceiling(m/3))/3).
%e A279408 T(7,7)=7 can be reached by:
%e A279408 ...K...
%e A279408 ......K
%e A279408 ..K....
%e A279408 .....K.
%e A279408 .K.....
%e A279408 ....K..
%e A279408 K......
%t A279408 Flatten[Table[Ceiling[Max[m Ceiling[n/3], n Ceiling[m/3]]/3],{n, 1, 13}, {m, 1, n}]] (* _Indranil Ghosh_, Mar 09 2017 *)
%o A279408 (PARI) T(n,m) = ceil(max(m*ceil(n/3), n*ceil(m/3))/3)
%o A279408 for(n=1,20,for(m=1,n, print1(T(n,m)", "))) \\ _Charles R Greathouse IV_, Dec 16 2016
%Y A279408 Cf. A075561, A279402, A279407, A279209.
%K A279408 nonn,tabl,easy
%O A279408 1,7
%A A279408 _Andrey Zabolotskiy_, Dec 16 2016