%I #4 Dec 14 2016 09:32:28
%S 0,0,0,2,4,2,4,46,46,4,14,384,1168,384,14,40,2894,23610,23610,2894,40,
%T 120,20444,456846,1280440,456846,20444,120,352,138944,8451524,
%U 66239560,66239560,8451524,138944,352,1032,918744,152161078,3300066400,9202124094
%N T(n,k)=Number of nXk 0..2 arrays with no element equal to a strict majority of its horizontal and vertical 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.......4..........46.............384..............2894..............20444
%C ....2......46........1168...........23610............456846............8451524
%C ....4.....384.......23610.........1280440..........66239560.........3300066400
%C ...14....2894......456846........66239560........9202124094......1236882205974
%C ...40...20444.....8451524......3300066400.....1236882205974....449916256454948
%C ..120..138944...152161078....160408991208...162587780938059.160287240382480502
%C ..352..918744..2683339202...7651924962192.21008453040002014
%C .1032.5954690.46585256882.359787825135858
%H R. H. Hardin, <a href="/A279527/b279527.txt">Table of n, a(n) for n = 1..83</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 8]
%F k=3: [order 22]
%e Some solutions for n=3 k=4
%e ..0..1..1..0. .0..1..2..2. .0..1..2..2. .0..0..1..2. .0..1..2..0
%e ..1..0..1..1. .1..0..0..0. .0..1..0..1. .2..2..0..2. .2..1..1..2
%e ..2..2..0..2. .0..2..0..1. .1..2..0..0. .1..1..0..2. .2..1..2..1
%Y Column 1 is A279322.
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Dec 14 2016