A209726 - OEIS

%I #8 Jul 12 2018 20:26:29

%S 16,17,18,20,22,26,30,38,46,62,78,110,142,206,270,398,526,782,1038,

%T 1550,2062,3086,4110,6158,8206,12302,16398,24590,32782,49166,65550,

%U 98318,131086,196622,262158,393230,524302,786446,1048590,1572878,2097166

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

%C Column 7 of A209727.

%H R. H. Hardin, <a href="/A209726/b209726.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).

%F Conjectures from _Colin Barker_, Jul 12 2018: (Start)

%F G.f.: x*(16 + x - 31*x^2) / ((1 - x)*(1 - 2*x^2)).

%F a(n) = 3*2^(n/2 - 1) + 14 for n even.

%F a(n) = 2^((n + 1)/2) + 14 for n odd.

%F (End)

%e Some solutions for n=4:

%e ..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 ..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 ..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 ..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 ..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 Cf. A209727.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 12 2012