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A279134 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

%I A279134 #4 Dec 06 2016 19:03:08
%S A279134 0,1,1,0,0,0,3,9,9,3,3,34,66,34,3,9,87,256,256,87,9,15,194,820,1324,
%T A279134 820,194,15,31,400,2551,6396,6396,2551,400,31,57,790,7491,30074,47452,
%U A279134 30074,7491,790,57,108,1511,21131,129264,316516,316516,129264,21131,1511,108
%N A279134 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
%C A279134 Table starts
%C A279134 ...0....1......0.......3.........3...........9...........15.............31
%C A279134 ...1....0......9......34........87.........194..........400............790
%C A279134 ...0....9.....66.....256.......820........2551.........7491..........21131
%C A279134 ...3...34....256....1324......6396.......30074.......129264.........535814
%C A279134 ...3...87....820....6396.....47452......316516......2017028.......12376570
%C A279134 ...9..194...2551...30074....316516.....3125600.....29410145......266502710
%C A279134 ..15..400...7491..129264...2017028....29410145....409061044.....5488392521
%C A279134 ..31..790..21131..535814..12376570...266502710...5488392521...109117856920
%C A279134 ..57.1511..57971.2150797..73672888..2346800921..71618045798..2111166039927
%C A279134 .108.2830.155551.8418336.428568648.20197483932.913912909445.39962431131266
%H A279134 R. H. Hardin, <a href="/A279134/b279134.txt">Table of n, a(n) for n = 1..180</a>
%F A279134 Empirical for column k:
%F A279134 k=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6)
%F A279134 k=2: [order 8] for n>9
%F A279134 k=3: [order 11] for n>17
%F A279134 k=4: [order 43] for n>50
%F A279134 k=5: [order 88] for n>108
%e A279134 Some solutions for n=4 k=4
%e A279134 ..0..0..1..0. .0..0..0..1. .0..1..0..1. .0..1..0..1. .0..0..1..0
%e A279134 ..1..0..1..1. .1..1..1..0. .0..0..1..0. .1..0..1..0. .1..1..0..1
%e A279134 ..1..1..0..0. .0..0..0..1. .0..1..0..0. .0..1..1..0. .1..0..1..0
%e A279134 ..1..0..1..1. .1..0..1..0. .1..0..1..0. .0..1..0..0. .0..0..0..1
%Y A279134 Column 1 is A105423(n-2).
%K A279134 nonn,tabl
%O A279134 1,7
%A A279134 _R. H. Hardin_, Dec 06 2016