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T(n,k)=Equals two maps: number of nXk binary arrays indicating the locations of corresponding elements equal to exactly two of their king-move neighbors in a random 0..1 nXk array
5

%I #4 Dec 08 2012 14:21:25

%S 1,1,1,2,5,2,4,18,18,4,7,37,143,37,7,12,85,816,816,85,12,21,184,4467,

%T 7140,4467,184,21,37,393,27192,64258,64258,27192,393,37,65,826,158296,

%U 660677,942945,660677,158296,826,65,114,1726,915920,6228324,16925474

%N T(n,k)=Equals two maps: number of nXk binary arrays indicating the locations of corresponding elements equal to exactly two of their king-move neighbors in a random 0..1 nXk array

%C Table starts

%C ...1....1.......2........4.........7........12........21.......37........65

%C ...1....5......18.......37........85.......184.......393......826......1726

%C ...2...18.....143......816......4467.....27192....158296...915920...5443662

%C ...4...37.....816.....7140.....64258....660677...6228324.59704733.580593280

%C ...7...85....4467....64258....942945..16925474.267978208

%C ..12..184...27192...660677..16925474.535851061

%C ..21..393..158296..6228324.267978208

%C ..37..826..915920.59704733

%C ..65.1726.5443662

%C .114.3568

%C .200

%H R. H. Hardin, <a href="/A220247/b220247.txt">Table of n, a(n) for n = 1..70</a>

%e Some solutions for n=3 k=4

%e ..1..1..0..0....0..0..1..0....0..1..0..0....1..0..1..0....0..0..1..1

%e ..1..0..0..0....0..0..1..0....0..0..1..1....0..1..0..0....0..0..0..0

%e ..1..0..1..0....0..0..0..1....0..0..0..0....0..1..0..0....0..1..0..1

%Y Column 1 is A005251(n+1)

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_ Dec 08 2012