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A297876 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3 or 5 king-move adjacent elements, with upper left element zero. 8

%I

%S 0,0,0,0,1,0,0,3,3,0,0,2,0,2,0,0,11,3,3,11,0,0,13,0,10,0,13,0,0,34,3,

%T 20,20,3,34,0,0,65,6,68,80,68,6,65,0,0,123,23,185,231,231,185,23,123,

%U 0,0,266,68,561,579,887,579,561,68,266,0,0,499,205,1588,2437,3307,3307,2437

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3 or 5 king-move adjacent elements, with upper left element zero.

%C Table starts

%C .0...0..0....0....0.....0......0.......0........0.........0.........0

%C .0...1..3....2...11....13.....34......65......123.......266.......499

%C .0...3..0....3....0.....3......6......23.......68.......205.......572

%C .0...2..3...10...20....68....185.....561.....1588......4814.....14322

%C .0..11..0...20...80...231....579....2437.....7507.....26278.....91622

%C .0..13..3...68..231...887...3307...13910....55501....228947....947582

%C .0..34..6..185..579..3307..13778...69160...325394...1617897...7900112

%C .0..65.23..561.2437.13910..69160..428609..2364407..14043631..81562636

%C .0.123.68.1588.7507.55501.325394.2364407.15589226.109627764.757954739

%H R. H. Hardin, <a href="/A297876/b297876.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

%F k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4)

%F k=3: [order 17] for n>18

%F k=4: [order 52] for n>53

%e Some solutions for n=7 k=4

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

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

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

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

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

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

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

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Jan 07 2018

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Last modified July 30 17:04 EDT 2021. Contains 346359 sequences. (Running on oeis4.)