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A286849 Array read by antidiagonals: T(m,n) = number of minimal dominating sets in the n X m king graph. 8

%I #16 Aug 12 2017 13:42:11

%S 1,2,2,2,4,2,4,6,6,4,4,16,12,16,4,7,20,36,36,20,7,9,52,64,256,64,52,9,

%T 13,80,204,400,400,204,80,13,18,176,446,2704,971,2704,446,176,18,25,

%U 296,1184,6400,6486,6486,6400,1184,296,25

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

%H Andrew Howroyd, <a href="/A286849/b286849.txt">Table of n, a(n) for n = 1..153</a>

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimalDominatingSet.html">Minimal Dominating Set</a>

%e Array begins:

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

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

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

%e 1 | 1 2 2 4 4 7 9 13...

%e 2 | 2 4 6 16 20 52 80 176...

%e 3 | 2 6 12 36 64 204 446 1184...

%e 4 | 4 16 36 256 400 2704 6400 30976...

%e 5 | 4 20 64 400 971 6486 22177 112317...

%e 6 | 7 52 204 2704 6486 85405 351503 3082745...

%e 7 | 9 80 446 6400 22177 351503 1997448 21587536...

%e 8 | 13 176 1184 30976 112317 3082745 21587536 360584008...

%e ...

%Y Rows 1-2 are A253413, A286850.

%Y Main diagonal is A286881.

%Y Cf. A218663 (dominating sets), A245013 (independent), A286870 (irredundant).

%Y Cf. A286847 (grid graph).

%K nonn,tabl

%O 1,2

%A _Andrew Howroyd_, Aug 01 2017

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Last modified May 3 03:31 EDT 2024. Contains 372204 sequences. (Running on oeis4.)