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%I #4 Jan 18 2018 07:47:32
%S 0,1,1,1,4,1,2,18,18,2,3,52,56,52,3,5,174,223,223,174,5,8,604,849,996,
%T 849,604,8,13,2048,3387,5180,5180,3387,2048,13,21,6948,13075,26926,
%U 49850,26926,13075,6948,21,34,23652,51006,135226,384118,384118,135226,51006
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0.....1......1.......2.........3..........5............8............13
%C ..1.....4.....18......52.......174........604.........2048..........6948
%C ..1....18.....56.....223.......849.......3387........13075.........51006
%C ..2....52....223.....996......5180......26926.......135226........690918
%C ..3...174....849....5180.....49850.....384118......2837337......23616114
%C ..5...604...3387...26926....384118....3935913.....38706835.....445387553
%C ..8..2048..13075..135226...2837337...38706835....509195874....8032883165
%C .13..6948..51006..690918..23616114..445387553...8032883165..190487814086
%C .21.23652.199243.3547086.189866553.4869394793.118750882425.4054091346048
%H R. H. Hardin, <a href="/A298389/b298389.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%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 20] for n>21
%F k=4: [order 69] for n>71
%e Some solutions for n=5 k=4
%e ..0..1..0..1. .0..0..0..1. .0..0..1..0. .0..1..0..1. .0..0..1..1
%e ..1..0..1..0. .1..1..1..0. .0..1..1..0. .1..0..0..1. .1..0..1..1
%e ..1..0..1..0. .1..0..0..1. .1..0..0..0. .1..0..0..0. .0..1..1..1
%e ..1..1..0..1. .0..1..0..1. .0..1..1..1. .1..0..0..1. .1..0..1..1
%e ..1..0..1..1. .0..0..1..1. .1..0..0..0. .0..1..0..1. .0..0..1..1
%Y Column 1 is A000045(n-1).
%Y Column 2 is A297945.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 18 2018