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A098604 Triangle T(n,k) read by rows, for 1 <= k <= n: minimal number of knights needed to cover a k X n board.

%I A098604 #25 Feb 16 2025 08:32:54
%S A098604 1,2,4,3,4,4,4,4,4,4,5,4,4,4,5,6,4,4,4,6,8,7,6,6,6,7,8,10,8,8,8,8,8,8,
%T A098604 11,12,9,8,8,8,8,10,12,13,14,10,8,8,8,9,12,14,14,15,16,11,8,8,8,10,12,
%U A098604 15,16,17,19,21,12,8,8,8,10,12,16,16,18,20,22,24,13,10,10,10,12,14
%N A098604 Triangle T(n,k) read by rows, for 1 <= k <= n: minimal number of knights needed to cover a k X n board.
%C A098604 How many knights are needed to occupy or attack every square of a k X n board?
%C A098604 I do not know how many of these numbers have been proved to be optimal. - _N. J. A. Sloane_, Nov 08 2004
%H A098604 Lee Morgenstern, <a href="https://web.archive.org/web/20070102070601/http://home.earthlink.net/~morgenstern/">Knight Domination</a>.
%H A098604 Frank Rubin, <a href="http://www.contestcen.com/knight.htm">Knight coverings for large chessboards</a>, 2000.
%H A098604 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KnightsProblem.html">Knights Problem</a>.
%e A098604 Triangle (with rows n >= 1 and columns k >= 1) begins as follows:
%e A098604   1
%e A098604   2 4
%e A098604   3 4 4
%e A098604   4 4 4 4
%e A098604   5 4 4 4 5
%e A098604   6 4 4 4 6 8
%e A098604   7 6 6 6 7 8 10
%e A098604   ...
%Y A098604 See A006075 for the n X n case (the main diagonal). A006076 gives number of ways to cover an n X n board using the minimal number of knights.
%K A098604 nonn,tabl,nice
%O A098604 1,2
%A A098604 _N. J. A. Sloane_
%E A098604 Morgenstern's table extends a long way beyond what is shown here.