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A207149 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. 9

%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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Last modified February 1 14:34 EST 2023. Contains 359993 sequences. (Running on oeis4.)