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%I #4 Dec 20 2016 10:55:31
%S 0,0,0,2,4,2,2,10,10,2,8,24,49,24,8,14,54,168,168,54,14,36,116,557,
%T 972,557,116,36,74,250,1758,5200,5200,1758,250,74,168,528,5441,26632,
%U 44893,26632,5441,528,168,358,1118,16500,134898,373516,373516,134898,16500
%N T(n,k)=Number of nXk 0..2 arrays with no element unequal 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........2..........8..........14..........36..........74
%C ...0....4.....10.......24.........54.........116.........250.........528
%C ...2...10.....49......168........557........1758........5441.......16500
%C ...2...24....168......972.......5200.......26632......134898......668668
%C ...8...54....557.....5200......44893......373516.....3010179....23836450
%C ..14..116...1758....26632.....373516.....4989784....64921744...827573664
%C ..36..250...5441...134898....3010179....64921744..1356293555.27796618392
%C ..74..528..16500...668668...23836450...827573664.27796618392
%C .168.1118..49253..3278294..185854745.10392951988
%C .358.2348.145290.15902088.1432781380
%H R. H. Hardin, <a href="/A279856/b279856.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -4*a(n-4) for n>5
%F k=2: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +4*a(n-5)
%F k=3: a(n) = 4*a(n-1) -2*a(n-2) -9*a(n-4) -4*a(n-5) -4*a(n-6) for n>9
%F k=4: [order 38] for n>41
%e Some solutions for n=4 k=4
%e ..0..1..1..1. .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1
%e ..0..1..1..1. .0..0..1..1. .0..0..0..1. .1..1..0..1. .0..0..0..1
%e ..2..2..1..1. .0..2..2..1. .2..0..0..1. .1..1..0..0. .0..0..0..1
%e ..2..2..2..2. .0..2..2..1. .0..0..0..1. .0..0..0..0. .0..0..1..1
%Y Column 1 is A219754(n+1)*2.
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Dec 20 2016
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