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%I #4 Dec 09 2016 15:35:40
%S 0,1,1,0,0,0,3,12,12,3,6,104,498,104,6,24,872,14908,14908,872,24,72,
%T 8064,396904,1160588,396904,8064,72,232,71680,10073670,85082276,
%U 85082276,10073670,71680,232,720,635312,246262496,6048938846,17784685668
%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 two elements, and with new values introduced in order 0 sequentially upwards.
%C Table starts
%C ....0.......1..........0............3.............6............24
%C ....1.......0.........12..........104...........872..........8064
%C ....0......12........498........14908........396904......10073670
%C ....3.....104......14908......1160588......85082276....6048938846
%C ....6.....872.....396904.....85082276...17784685668.3593187600532
%C ...24....8064...10073670...6048938846.3593187600532
%C ...72...71680..246262496.417999641840
%C ..232..635312.5863622944
%C ..720.5554240
%C .2232
%H R. H. Hardin, <a href="/A279305/b279305.txt">Table of n, a(n) for n = 1..60</a>
%F Empirical for column k:
%F k=1: a(n) = 6*a(n-1) -6*a(n-2) -16*a(n-3) +12*a(n-4) +24*a(n-5) +8*a(n-6) for n>8
%F k=2: [order 15] for n>16
%F k=3: [order 51] for n>54
%e Some solutions for n=3 k=4
%e ..0..0..1..1. .0..1..1..0. .0..1..1..1. .0..0..1..0. .0..1..1..0
%e ..1..0..1..0. .2..1..1..2. .2..2..0..1. .1..1..0..0. .2..0..2..1
%e ..2..2..0..1. .2..0..1..0. .1..0..0..2. .1..0..2..2. .0..0..0..2
%K nonn,tabl
%O 1,7
%A _R. H. Hardin_, Dec 09 2016
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