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Array read by antidiagonals: T(m,n) = number of irredundant sets in the m X n king graph.
5

%I #17 Feb 16 2025 08:33:45

%S 2,3,3,5,5,5,9,11,11,9,15,25,43,25,15,26,51,133,133,51,26,44,113,463,

%T 647,463,113,44,76,235,1493,2945,2945,1493,235,76,130,521,5011,14217,

%U 22049,14217,5011,521,130,223,1107,16659,65627,147672,147672,65627,16659,1107,223

%N Array read by antidiagonals: T(m,n) = number of irredundant sets in the m X n king graph.

%H Andrew Howroyd, <a href="/A286870/b286870.txt">Table of n, a(n) for n = 1..153</a>

%H Matthew D. Kearse and Peter B. Gibbons, <a href="http://hdl.handle.net/2292/3642">Computational Methods and New Results for Chessboard Problems</a>, CDMTCS Research Reports CDMTCS-133 (2000).

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KingGraph.html">King Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IrredundantSet.html">Irredundant Set</a>

%e Array begins:

%e ====================================================================

%e m\n| 1 2 3 4 5 6 7 8

%e ---|----------------------------------------------------------------

%e 1 | 2 3 5 9 15 26 44 76...

%e 2 | 3 5 11 25 51 113 235 521...

%e 3 | 5 11 43 133 463 1493 5011 16659...

%e 4 | 9 25 133 647 2945 14217 65627 322163...

%e 5 | 15 51 463 2945 22049 147672 1043127 7365740...

%e 6 | 26 113 1493 14217 147672 1455385 14656628 151865727...

%e 7 | 44 235 5011 65627 1043127 14656628 218691097 3287831848...

%e 8 | 76 521 16659 322163 7365740 151865727 3287831848 72877697369...

%e ...

%Y Row 1 is A286887.

%Y Main diagonal is A286871.

%Y Cf. A218663 (dominating sets), A286849 (minimal dominating sets).

%Y Cf. A286868 (grid graph).

%K nonn,tabl,changed

%O 1,1

%A _Andrew Howroyd_, Aug 02 2017