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%I #4 May 05 2018 15:21:42
%S 0,1,1,1,3,1,2,11,11,2,3,10,6,10,3,5,51,18,18,51,5,8,165,32,26,32,165,
%T 8,13,306,60,155,155,60,306,13,21,993,124,427,596,427,124,993,21,34,
%U 2867,288,1122,1641,1641,1122,288,2867,34,55,6818,598,4109,5415,3434,5415
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4 or 5 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0....1...1.....2......3......5.......8.......13........21.........34
%C ..1....3..11....10.....51....165.....306......993......2867.......6818
%C ..1...11...6....18.....32.....60.....124......288.......598.......1266
%C ..2...10..18....26....155....427....1122.....4109.....13836......42480
%C ..3...51..32...155....596...1641....5415....30207....124598.....500772
%C ..5..165..60...427...1641...3434...13624....69126....260517....1102813
%C ..8..306.124..1122...5415..13624...77360...478889...2630794...17166221
%C .13..993.288..4109..30207..69126..478889..4890117..30295907..239161610
%C .21.2867.598.13836.124598.260517.2630794.30295907.181435839.1835718615
%H R. H. Hardin, <a href="/A304058/b304058.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = a(n-1) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6
%F k=3: [order 15] for n>18
%F k=4: [order 57] for n>60
%e Some solutions for n=5 k=4
%e ..0..0..1..0. .0..1..0..1. .0..1..1..0. .0..0..1..0. .0..0..0..1
%e ..1..0..0..1. .0..0..1..1. .0..1..1..0. .1..0..0..1. .1..0..0..1
%e ..0..0..0..0. .0..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e ..1..0..0..1. .0..1..1..0. .0..0..0..0. .1..0..0..1. .1..0..0..1
%e ..0..0..0..1. .1..1..1..1. .0..1..1..0. .1..0..0..0. .0..1..0..0
%Y Column 1 is A000045(n-1).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, May 05 2018
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