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%I
%S 50,30,30,80,48,80,62,56,56,62,159,95,157,95,159,122,110,110,110,110,
%T 122,315,187,311,190,311,187,315,242,218,218,218,218,218,218,242,628,
%U 371,619,374,622,374,619,371,628,482,434,434,434,434,434,434,434,434,482,1254
%N T(n,k) = Number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor.
%C Table starts
%C ..50..30..80..62..159..122..315..242..628..482.1254...962..2506..1922..5010
%C ..30..48..56..95..110..187..218..371..434..740..866..1478..1730..2954..3458
%C ..80..56.157.110..311..218..619..434.1235..866.2468..1730..4934..3458..9866
%C ..62..95.110.190..218..374..434..742..866.1478.1730..2954..3458..5906..6914
%C .159.110.311.218..622..434.1238..866.2470.1730.4934..3458..9866..6914.19730
%C .122.187.218.374..434..754..866.1490.1730.2962.3458..5906..6914.11810.13826
%C .315.218.619.434.1238..866.2482.1730.4946.3458.9874..6914.19730.13826.39458
%C .242.371.434.742..866.1490.1730.3010.3458.5954.6914.11842.13826.23618.27650
%H R. H. Hardin, <a href="/A207149/b207149.txt">Table of n, a(n) for n = 1..868</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) for n > 8;
%F k=2: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) for n > 9;
%F k=3: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) for n > 10;
%F k=4: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) for n > 11;
%F k=5: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) for n > 12;
%F k=6: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) for n > 13;
%F k=7: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) for n > 14;
%F Apparently a(n) = a(n-1) +2*a(n-2) -2*a(n-3) for n > k+7.
%e Some solutions for n=4, k=3
%e ..2..0..1..0....1..0..2..0....2..1..0..2....1..1..0..1....1..0..1..0
%e ..0..2..0..1....0..1..0..2....1..0..1..0....1..0..1..0....0..1..0..1
%e ..1..0..2..0....1..0..1..0....0..1..0..1....0..1..0..1....1..0..1..0
%e ..0..1..0..2....0..1..0..1....1..0..1..0....2..0..1..0....0..1..0..1
%e ..2..0..1..2....1..0..1..2....0..1..0..1....0..2..0..1....1..0..1..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Feb 15 2012
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