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A209726 1/4 the number of (n+1) X 8 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.

%I A209726 #8 Jul 12 2018 20:26:29
%S A209726 16,17,18,20,22,26,30,38,46,62,78,110,142,206,270,398,526,782,1038,
%T A209726 1550,2062,3086,4110,6158,8206,12302,16398,24590,32782,49166,65550,
%U A209726 98318,131086,196622,262158,393230,524302,786446,1048590,1572878,2097166
%N A209726 1/4 the number of (n+1) X 8 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.
%C A209726 Column 7 of A209727.
%H A209726 R. H. Hardin, <a href="/A209726/b209726.txt">Table of n, a(n) for n = 1..210</a>
%F A209726 Empirical: a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3).
%F A209726 Conjectures from _Colin Barker_, Jul 12 2018: (Start)
%F A209726 G.f.: x*(16 + x - 31*x^2) / ((1 - x)*(1 - 2*x^2)).
%F A209726 a(n) = 3*2^(n/2 - 1) + 14 for n even.
%F A209726 a(n) = 2^((n + 1)/2) + 14 for n odd.
%F A209726 (End)
%e A209726 Some solutions for n=4:
%e A209726 ..1..2..0..2..1..2..0..2....0..1..0..2..0..1..0..2....1..2..0..2..0..2..1..2
%e A209726 ..2..0..1..0..2..0..1..0....2..0..2..1..2..0..2..1....2..0..1..0..1..0..2..0
%e A209726 ..1..2..0..2..1..2..0..2....0..1..0..2..0..1..0..2....1..2..0..2..0..2..1..2
%e A209726 ..2..0..1..0..2..0..1..0....2..0..2..1..2..0..2..1....2..0..1..0..1..0..2..0
%e A209726 ..1..2..0..2..1..2..0..2....0..1..0..2..0..1..0..2....1..2..0..2..0..2..1..2
%Y A209726 Cf. A209727.
%K A209726 nonn
%O A209726 1,1
%A A209726 _R. H. Hardin_, Mar 12 2012