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%I #4 Jan 23 2018 12:12:55
%S 0,1,1,0,4,0,1,4,4,1,0,16,0,16,0,1,48,7,7,48,1,0,88,7,83,7,88,0,1,240,
%T 25,218,218,25,240,1,0,704,88,682,1893,682,88,704,0,1,1600,187,4068,
%U 5749,5749,4068,187,1600,1,0,4032,491,14719,51213,32834,51213,14719,491,4032
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .0....1...0.....1.......0........1..........0...........1.............0
%C .1....4...4....16......48.......88........240.........704..........1600
%C .0....4...0.....7.......7.......25.........88.........187...........491
%C .1...16...7....83.....218......682.......4068.......14719.........58834
%C .0...48...7...218....1893.....5749......51213......407430.......2021867
%C .1...88..25...682....5749....32834.....480343.....4361690......38698593
%C .0..240..88..4068...51213...480343...10823065...161922923....2400592063
%C .1..704.187.14719..407430..4361690..161922923..4673855921...92707820639
%C .0.1600.491.58834.2021867.38698593.2400592063.92707820639.3376311711594
%H R. H. Hardin, <a href="/A298622/b298622.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-2)
%F k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5)
%F k=3: [order 19] for n>20
%F k=4: [order 64] for n>65
%e Some solutions for n=5 k=4
%e ..0..0..0..1. .0..1..0..0. .0..0..0..1. .0..0..1..1. .0..1..1..1
%e ..0..0..1..0. .0..1..0..0. .0..0..1..0. .0..0..1..1. .1..0..1..1
%e ..1..1..1..1. .1..1..0..0. .1..1..1..1. .0..0..1..1. .1..1..1..1
%e ..0..0..1..0. .1..1..1..1. .1..1..0..1. .1..0..1..1. .1..0..0..0
%e ..0..0..0..1. .0..0..1..1. .1..1..1..0. .1..0..1..1. .0..1..0..0
%Y Column 2 is A298448.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 23 2018
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