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%I #8 Oct 11 2018 09:01:55
%S 24,90,324,1188,4320,15768,57456,209520,763776,2784672,10152000,
%T 37012032,134936064,491944320,1793505024,6538675968,23838382080,
%U 86908819968,316847932416,1155148784640,4211385163776,15353663035392,55975637053440
%N Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock having the sum of the squares of the edge differences equal to 2.
%H R. H. Hardin, <a href="/A233637/b233637.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 6*a(n-2).
%F Conjectures from _Colin Barker_, Oct 11 2018: (Start)
%F G.f.: 6*x*(4 + 7*x) / (1 - 2*x - 6*x^2).
%F a(n) = ((1-sqrt(7))^n*(-17+7*sqrt(7)) + (1+sqrt(7))^n*(17+7*sqrt(7))) / (2*sqrt(7)).
%F (End)
%e Some solutions for n=5:
%e ..1..1....1..2....0..1....0..0....1..1....1..0....0..1....1..0....2..2....0..1
%e ..1..2....1..2....0..1....1..0....2..1....1..1....1..1....1..0....2..1....0..1
%e ..1..2....1..2....1..1....1..0....2..1....0..1....0..0....1..1....1..1....0..1
%e ..2..2....2..2....0..1....1..0....2..1....1..1....1..0....2..1....0..1....1..1
%e ..1..1....1..1....1..1....1..0....1..1....0..1....1..1....1..1....1..1....1..0
%e ..2..1....0..0....0..1....1..1....0..0....0..0....0..1....2..2....1..2....1..0
%Y Column 1 of A233644.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 14 2013