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%I #4 Feb 01 2018 14:37:03
%S 1,1,1,1,5,1,1,13,13,1,1,42,38,42,1,1,127,199,199,127,1,1,389,864,
%T 2096,864,389,1,1,1192,4366,17930,17930,4366,1192,1,1,3645,21804,
%U 175031,295407,175031,21804,3645,1,1,11161,111861,1718789,5558665,5558665
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1....1......1........1..........1............1..............1................1
%C .1....5.....13.......42........127..........389...........1192.............3645
%C .1...13.....38......199........864.........4366..........21804...........111861
%C .1...42....199.....2096......17930.......175031........1718789.........17101477
%C .1..127....864....17930.....295407......5558665......104819165.......1992248544
%C .1..389...4366...175031....5558665....199153610.....7165136807.....259511787831
%C .1.1192..21804..1718789..104819165...7165136807...491688804213...33934925502793
%C .1.3645.111861.17101477.1992248544.259511787831.33934925502793.4462148033879670
%H R. H. Hardin, <a href="/A299060/b299060.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) = a(n-1) +5*a(n-2) +4*a(n-3)
%F k=3: [order 14] for n>16
%F k=4: [order 38] for n>39
%e Some solutions for n=5 k=4
%e ..0..0..1..0. .0..0..1..1. .0..0..1..1. .0..0..1..0. .0..1..0..0
%e ..0..1..1..1. .0..0..1..1. .1..0..1..1. .0..0..1..1. .0..0..0..1
%e ..1..1..0..1. .1..0..0..0. .0..0..1..0. .0..0..1..1. .1..1..0..0
%e ..1..1..1..1. .1..1..0..1. .1..0..0..0. .0..0..0..1. .0..1..1..0
%e ..0..1..0..1. .1..1..1..1. .0..0..0..1. .0..1..0..0. .0..0..0..0
%Y Column 2 is A298234.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Feb 01 2018
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