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A282791 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its king-move neighbors, with the exception of exactly one element.

%I A282791 #4 Feb 21 2017 08:46:40
%S A282791 0,0,0,1,0,1,2,8,8,2,5,16,73,16,5,12,72,318,318,72,12,26,240,1747,
%T A282791 1952,1747,240,26,56,736,8216,16584,16584,8216,736,56,118,2352,38027,
%U A282791 119176,208559,119176,38027,2352,118,244,7128,173722,832218,2207352,2207352
%N A282791 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its king-move neighbors, with the exception of exactly one element.
%C A282791 Table starts
%C A282791 ...0.....0.......1.........2...........5............12..............26
%C A282791 ...0.....0.......8........16..........72...........240.............736
%C A282791 ...1.....8......73.......318........1747..........8216...........38027
%C A282791 ...2....16.....318......1952.......16584........119176..........832218
%C A282791 ...5....72....1747.....16584......208559.......2207352........22998587
%C A282791 ..12...240....8216....119176.....2207352......34974844.......545174028
%C A282791 ..26...736...38027....832218....22998587.....545174028.....12713143876
%C A282791 ..56..2352..173722...5780340...236744562....8385651160....292288389872
%C A282791 .118..7128..773529..39020884..2372235577..125782952202...6555156469894
%C A282791 .244.21424.3412416.260919192.23556868268.1869100531456.145619095090322
%H A282791 R. H. Hardin, <a href="/A282791/b282791.txt">Table of n, a(n) for n = 1..264</a>
%F A282791 Empirical for column k:
%F A282791 k=1: a(n) = 2*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6)
%F A282791 k=2: a(n) = 2*a(n-1) +5*a(n-2) +2*a(n-3) -17*a(n-4) -24*a(n-5) -16*a(n-6)
%F A282791 k=3: [order 12]
%F A282791 k=4: [order 18]
%F A282791 k=5: [order 42]
%F A282791 k=6: [order 60]
%e A282791 Some solutions for n=4 k=4
%e A282791 ..0..1..0..0. .0..1..0..1. .0..1..0..0. .0..0..1..1. .1..0..1..0
%e A282791 ..1..0..0..1. .0..0..1..0. .1..0..0..1. .0..1..0..0. .0..0..1..0
%e A282791 ..0..1..0..0. .1..0..0..0. .0..0..1..0. .0..0..0..1. .0..0..0..0
%e A282791 ..0..0..0..0. .1..0..1..0. .1..0..0..1. .0..1..0..0. .1..1..1..0
%Y A282791 Column 1 is A073778(n-1).
%K A282791 nonn,tabl
%O A282791 1,7
%A A282791 _R. H. Hardin_, Feb 21 2017