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%I #11 Jun 19 2018 12:25:11
%S 50,30,80,62,159,122,315,242,628,482,1254,962,2506,1922,5010,3842,
%T 10018,7682,20034,15362,40066,30722,80130,61442,160258,122882,320514,
%U 245762,641026,491522,1282050,983042,2564098,1966082,5128194,3932162,10256386
%N Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor.
%C Column 1 of A207149.
%H R. H. Hardin, <a href="/A207142/b207142.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) for n>8.
%F Conjectures from _Colin Barker_, Jun 19 2018: (Start)
%F G.f.: x*(50 - 20*x - 50*x^2 + 22*x^3 - 3*x^4 - x^5 - x^6 + x^7) / ((1 - x)*(1 - 2*x^2)).
%F a(n) = 15 * 2^(n/2) + 2 for n>5 and even.
%F a(n) = 313 * 2^((n-7)/2) + 2 for n>5 and odd.
%F (End)
%e Some solutions for n=4:
%e ..2..0....2..1....1..1....2..1....1..1....0..2....0..1....2..1....0..1....1..0
%e ..0..2....2..0....2..0....1..2....1..0....1..0....2..0....1..0....2..0....0..1
%e ..1..0....0..2....0..2....2..1....0..1....0..1....0..2....0..1....0..2....1..0
%e ..0..1....1..0....1..0....1..2....1..0....2..0....1..0....1..0....2..0....0..1
%e ..2..1....0..1....0..1....2..1....0..1....0..2....0..1....0..1....0..2....2..2
%Y Cf. A207149.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 15 2012
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