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%I #4 Jul 16 2018 13:02:20
%S 1,1,1,1,4,1,1,8,8,1,1,24,25,24,1,1,82,143,143,82,1,1,272,851,1719,
%T 851,272,1,1,908,5114,20235,20235,5114,908,1,1,3076,31197,242908,
%U 467377,242908,31197,3076,1,1,10444,191330,2937685,10973407,10973407,2937685
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1.....1.......1.........1............1..............1.................1
%C .1.....4.......8........24...........82............272...............908
%C .1.....8......25.......143..........851...........5114.............31197
%C .1....24.....143......1719........20235.........242908...........2937685
%C .1....82.....851.....20235.......467377.......10973407.........259460352
%C .1...272....5114....242908.....10973407......504420842.......23331389753
%C .1...908...31197...2937685....259460352....23331389753.....2110655397816
%C .1..3076..191330..35648580...6154985913..1082511783630...191524282642552
%C .1.10444.1175122.433015180.146148278604.50268964898040.17393755319723555
%H R. H. Hardin, <a href="/A316932/b316932.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6
%F k=3: [order 13] for n>15
%F k=4: [order 34] for n>35
%F k=5: [order 89] for n>92
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..1..0..0. .0..1..0..0. .0..1..0..0. .0..0..0..1
%e ..1..1..0..1. .0..1..1..1. .0..1..1..1. .1..0..1..1. .1..1..1..0
%e ..0..0..0..0. .1..0..0..1. .0..0..0..1. .0..1..0..0. .1..1..1..1
%e ..1..0..1..1. .1..1..0..0. .0..1..0..0. .0..1..0..0. .0..0..0..0
%e ..1..0..1..1. .0..1..0..1. .0..1..0..1. .0..1..0..0. .1..1..0..1
%Y Column 2 is A303882.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jul 16 2018
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