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A230184 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value 2-x(i,j).

%I A230184 #6 Jun 02 2025 08:42:30
%S A230184 0,3,0,3,9,0,9,27,33,0,15,159,231,129,0,33,825,3411,1971,513,0,63,
%T A230184 4395,44487,73857,16815,2049,0,129,23307,596973,2432241,1603431,
%U A230184 143451,8193,0,255,123729,7957785,82359177,133265847,34825803,1223799,32769,0,513
%N A230184 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value 2-x(i,j).
%C A230184 Table starts
%C A230184 .0.....3........3...........9.............15................33
%C A230184 .0.....9.......27.........159............825..............4395
%C A230184 .0....33......231........3411..........44487............596973
%C A230184 .0...129.....1971.......73857........2432241..........82359177
%C A230184 .0...513....16815.....1603431......133265847.......11393567289
%C A230184 .0..2049...143451....34825803.....7303192425.....1576417829097
%C A230184 .0..8193..1223799...756450105...400233701367...218117038953009
%C A230184 .0.32769.10440387.16430979183.21933865129257.30179260908320577
%H A230184 R. H. Hardin, <a href="/A230184/b230184.txt">Table of n, a(n) for n = 1..238</a>
%F A230184 Empirical for column k:
%F A230184 k=1: a(n) = a(n-1)
%F A230184 k=2: a(n) = 5*a(n-1) -4*a(n-2)
%F A230184 k=3: a(n) = 9*a(n-1) -4*a(n-2)
%F A230184 k=4: a(n) = 26*a(n-1) -97*a(n-2) +89*a(n-3) -18*a(n-4) +a(n-5)
%F A230184 k=5: [order 6] for n>8
%F A230184 k=6: [order 23] for n>24
%F A230184 k=7: [order 34] for n>37
%F A230184 Empirical for row n:
%F A230184 n=1: a(n) = a(n-1) +2*a(n-2)
%F A230184 n=2: a(n) = 4*a(n-1) +7*a(n-2) +a(n-3) -6*a(n-4) -5*a(n-5) for n>6
%F A230184 n=3: [order 21] for n>23
%F A230184 n=4: [order 93] for n>96
%e A230184 Some solutions for n=3 k=4
%e A230184 ..2..0..1..1....0..2..1..1....2..0..0..1....0..2..2..0....1..1..2..2
%e A230184 ..0..2..2..0....0..0..2..2....0..2..1..1....0..1..2..0....2..0..0..0
%e A230184 ..0..2..1..1....1..1..0..2....1..1..0..2....1..2..0..2....0..2..2..0
%Y A230184 Column 2 is A084508(n+1)
%Y A230184 Row 1 is A062510(n-1)
%K A230184 nonn,tabl
%O A230184 1,2
%A A230184 _R. H. Hardin_, Oct 11 2013