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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.

%I A297876 #4 Jan 07 2018 11:32:11
%S A297876 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 A297876 20,20,3,34,0,0,65,6,68,80,68,6,65,0,0,123,23,185,231,231,185,23,123,
%U A297876 0,0,266,68,561,579,887,579,561,68,266,0,0,499,205,1588,2437,3307,3307,2437
%N 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.
%C A297876 Table starts
%C A297876 .0...0..0....0....0.....0......0.......0........0.........0.........0
%C A297876 .0...1..3....2...11....13.....34......65......123.......266.......499
%C A297876 .0...3..0....3....0.....3......6......23.......68.......205.......572
%C A297876 .0...2..3...10...20....68....185.....561.....1588......4814.....14322
%C A297876 .0..11..0...20...80...231....579....2437.....7507.....26278.....91622
%C A297876 .0..13..3...68..231...887...3307...13910....55501....228947....947582
%C A297876 .0..34..6..185..579..3307..13778...69160...325394...1617897...7900112
%C A297876 .0..65.23..561.2437.13910..69160..428609..2364407..14043631..81562636
%C A297876 .0.123.68.1588.7507.55501.325394.2364407.15589226.109627764.757954739
%H A297876 R. H. Hardin, <a href="/A297876/b297876.txt">Table of n, a(n) for n = 1..220</a>
%F A297876 Empirical for column k:
%F A297876 k=1: a(n) = a(n-1)
%F A297876 k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4)
%F A297876 k=3: [order 17] for n>18
%F A297876 k=4: [order 52] for n>53
%e A297876 Some solutions for n=7 k=4
%e A297876 ..0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0
%e A297876 ..0..1..0..1. .0..1..1..0. .1..0..1..0. .0..0..0..0. .0..0..0..0
%e A297876 ..0..1..1..0. .1..0..1..0. .1..1..0..0. .1..1..1..1. .1..1..1..1
%e A297876 ..0..1..0..1. .1..0..0..1. .1..0..1..0. .1..0..0..1. .1..0..0..1
%e A297876 ..0..1..0..1. .1..1..1..1. .1..0..0..1. .0..1..0..1. .0..0..1..0
%e A297876 ..0..1..0..1. .0..0..0..0. .1..0..1..0. .0..1..1..0. .1..0..0..1
%e A297876 ..0..0..1..1. .0..0..0..0. .1..1..0..0. .0..0..0..0. .1..1..1..1
%K A297876 nonn,tabl
%O A297876 1,8
%A A297876 _R. H. Hardin_, Jan 07 2018