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A298139 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.

%I A298139 #4 Jan 13 2018 11:15:16
%S A298139 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 A298139 20,20,3,34,0,0,65,6,68,88,68,6,65,0,0,123,23,185,242,242,185,23,123,
%U A298139 0,0,266,68,561,627,917,627,561,68,266,0,0,499,205,1600,2604,3417,3417,2604
%N A298139 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.
%C A298139 Table starts
%C A298139 .0...0..0....0....0.....0......0.......0........0.........0.........0
%C A298139 .0...1..3....2...11....13.....34......65......123.......266.......499
%C A298139 .0...3..0....3....0.....3......6......23.......68.......205.......572
%C A298139 .0...2..3...10...20....68....185.....561.....1600......4856.....14490
%C A298139 .0..11..0...20...88...242....627....2604.....8137.....28727....101137
%C A298139 .0..13..3...68..242...917...3417...14533....58845....244155...1024766
%C A298139 .0..34..6..185..627..3417..14422...73961...354200...1772595...8807624
%C A298139 .0..65.23..561.2604.14533..73961..467043..2633905..15796516..93682029
%C A298139 .0.123.68.1600.8137.58845.354200.2633905.17828062.127068717.899366629
%H A298139 R. H. Hardin, <a href="/A298139/b298139.txt">Table of n, a(n) for n = 1..220</a>
%F A298139 Empirical for column k:
%F A298139 k=1: a(n) = a(n-1)
%F A298139 k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4)
%F A298139 k=3: [order 17] for n>18
%F A298139 k=4: [order 60] for n>61
%e A298139 Some solutions for n=7 k=4
%e A298139 ..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..0..0
%e A298139 ..0..1..1..0. .0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..1..0
%e A298139 ..1..1..0..1. .1..0..1..1. .0..1..0..1. .0..1..0..1. .1..0..1..0
%e A298139 ..1..0..1..0. .0..1..0..1. .1..0..1..0. .1..0..0..1. .1..0..1..0
%e A298139 ..1..0..0..0. .0..0..0..1. .1..0..1..0. .0..1..0..1. .0..1..1..0
%e A298139 ..0..1..1..0. .0..1..1..0. .1..0..0..1. .0..1..1..0. .1..0..1..0
%e A298139 ..0..0..1..1. .1..1..0..0. .1..1..1..1. .0..0..0..0. .1..1..0..0
%Y A298139 Column 2 is A297870.
%Y A298139 Column 3 is A297871.
%K A298139 nonn,tabl
%O A298139 1,8
%A A298139 _R. H. Hardin_, Jan 13 2018