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%I #6 Oct 01 2021 16:40:19
%S 0,1,0,0,3,0,3,27,24,0,6,254,734,232,0,24,2301,19986,20448,2232,0,72,
%T 19053,498424,1546164,549608,20880,0,232,149696,11256083,104452983,
%U 113887852,14309072,190656,0,720,1124969,239891281,6415919752
%N T(n,k) = Number of n X k 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal 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 .0.......3.........27............254...............2301.................19053
%C .0......24........734..........19986.............498424..............11256083
%C .0.....232......20448........1546164..........104452983............6415919752
%C .0....2232.....549608......113887852........20868369045.........3484404510555
%C .0...20880...14309072.....8077041000......4019412007893......1824673552805793
%C .0..190656..362942080...556408163556....752482408442895....928920011450982106
%C .0.1707264.9010004672.37457887289336.137719420200247895.462385405050721564618
%H R. H. Hardin, <a href="/A279657/b279657.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: [order 6] for n>7.
%F k=3: [order 9] for n>10.
%F k=4: [order 24] for n>25.
%F k=5: [order 42] for n>43.
%F Empirical for row n:
%F n=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 n=2: [order 13].
%F n=3: [order 51] for n>53.
%e Some solutions for n=3, k=4
%e ..0..0..0..1. .0..0..1..2. .0..0..0..1. .0..0..1..2. .0..1..0..2
%e ..2..1..1..0. .0..1..2..2. .0..2..2..0. .0..1..2..0. .2..1..1..0
%e ..1..0..1..2. .2..1..0..2. .0..0..2..1. .2..0..2..1. .1..2..0..0
%Y Row 1 is A279300.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Dec 16 2016
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