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%I #4 Dec 09 2016 23:01:43
%S 0,0,0,2,0,2,4,16,16,4,14,152,664,152,14,40,1536,16092,16092,1536,40,
%T 120,13776,384180,1079496,384180,13776,120,352,118664,8854880,
%U 73482624,73482624,8854880,118664,352,1032,991616,198179722,4808164964
%N T(n,k)=Number of nXk 0..2 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
%C Table starts
%C ....0........0...........2..............4..............14...............40
%C ....0........0..........16............152............1536............13776
%C ....2.......16.........664..........16092..........384180..........8854880
%C ....4......152.......16092........1079496........73482624.......4808164964
%C ...14.....1536......384180.......73482624.....14012963052....2584102824124
%C ...40....13776.....8854880.....4808164964...2584102824124.1348916804333952
%C ..120...118664...198179722...306703795184.466109368455794
%C ..352...991616..4349449420.19222109104916
%C .1032..8109024.94030021118
%C .3008.65252928
%H R. H. Hardin, <a href="/A279327/b279327.txt">Table of n, a(n) for n = 1..71</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4) for n>5
%F k=2: [order 10]
%F k=3: [order 34] for n>35
%e Some solutions for n=3 k=4
%e ..0..0..1..0. .0..1..2..0. .0..1..2..1. .0..1..0..1. .0..1..2..0
%e ..0..1..2..1. .0..0..2..1. .2..2..0..0. .0..2..1..2. .1..2..0..0
%e ..2..2..0..1. .2..1..1..2. .1..2..1..0. .1..0..1..1. .0..2..2..1
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Dec 09 2016
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