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%I #6 Jan 29 2018 05:14:40
%S 1,1,1,1,4,1,1,4,4,1,1,8,1,8,1,1,36,2,2,36,1,1,52,14,3,14,52,1,1,100,
%T 10,41,41,10,100,1,1,356,12,38,480,38,12,356,1,1,628,72,70,374,374,70,
%U 72,628,1,1,1220,82,374,1055,174,1055,374,82,1220,1,1,3668,90,664,9880,604
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 4, 5 or 7 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1...1..1...1.....1....1.....1......1......1.......1........1.........1
%C .1...4..4...8....36...52...100....356....628....1220.....3668......7268
%C .1...4..1...2....14...10....12.....72.....82......90......400.......600
%C .1...8..2...3....41...38....70....374....664....1327.....4668.....10974
%C .1..36.14..41...480..374..1055...9880..11792...31779...239375....376486
%C .1..52.10..38...374..174...604...5381...5527...16221...110018....190453
%C .1.100.12..70..1055..604..2888..28278..43961..164865..1297974...3202666
%C .1.356.72.374..9880.5381.28278.582062.684296.3320171.49103067..98469245
%C .1.628.82.664.11792.5527.43961.684296.939451.6179745.77845252.205903671
%H R. H. Hardin, <a href="/A298575/b298575.txt">Table of n, a(n) for n = 1..241</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1) +8*a(n-3) -4*a(n-4)
%F k=3: a(n) = 7*a(n-3) +2*a(n-4) +a(n-5) -10*a(n-6) -2*a(n-7) -2*a(n-8) +2*a(n-9) with g.f. (1+3*x^2-8*x^3)/(1-x-8*x^3+4*x^4).
%F k=4: [order 32] for n>33
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..0..1..0. .0..1..1..1. .0..1..1..1. .0..0..1..0
%e ..1..1..1..1. .1..0..1..1. .1..1..1..0. .1..1..1..0. .1..0..1..1
%e ..1..1..1..1. .0..0..1..1. .0..0..0..0. .1..1..1..1. .1..1..1..1
%e ..1..1..0..1. .0..0..1..0. .0..1..0..0. .1..1..0..0. .0..0..1..0
%e ..0..1..0..0. .1..0..1..1. .1..1..0..1. .0..1..0..1. .1..0..1..1
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 22 2018
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