%I #4 Dec 15 2016 11:04:47
%S 0,0,0,2,4,0,4,36,40,0,14,304,944,352,0,40,2212,20776,23072,3008,0,
%T 120,15428,406200,1356120,547168,25280,0,352,103648,7630156,72177144,
%U 86246944,12701248,209792,0,1032,680052,138602548,3684310576,12490527012
%N T(n,k)=Number of nXk 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal 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.........36............304..............2212.................15428
%C .0......40........944..........20776............406200...............7630156
%C .0.....352......23072........1356120..........72177144............3684310576
%C .0....3008.....547168.......86246944.......12490527012.........1732429706176
%C .0...25280...12701248.....5385546376.....2121871518232.......800037452999320
%C .0..209792..290067328...331573929104...355347019237332....364333887872124232
%C .0.1723392.6540226304.20185283466808.58835479020749472.164074884296083732404
%H R. H. Hardin, <a href="/A279580/b279580.txt">Table of n, a(n) for n = 1..110</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 16*a(n-1) -72*a(n-2) +64*a(n-3) -16*a(n-4)
%F k=3: [order 6] for n>7
%F k=4: [order 16] for n>17
%F k=5: [order 28] for n>29
%F Empirical for row n:
%F n=1: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4) for n>5
%F n=2: [order 8]
%F n=3: [order 34] for n>35
%e Some solutions for n=3 k=4
%e ..0..0..1..0. .0..1..1..1. .0..1..1..2. .0..1..2..1. .0..1..2..1
%e ..1..2..1..2. .2..0..0..0. .1..0..0..2. .0..2..2..2. .1..0..0..2
%e ..0..1..0..2. .0..2..2..0. .2..0..2..1. .1..2..1..0. .0..2..2..1
%Y Row 1 is A279322.
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Dec 15 2016