A209725 - OEIS

%I #8 Jul 12 2018 09:15:35

%S 12,13,14,16,18,22,26,34,42,58,74,106,138,202,266,394,522,778,1034,

%T 1546,2058,3082,4106,6154,8202,12298,16394,24586,32778,49162,65546,

%U 98314,131082,196618,262154,393226,524298,786442,1048586,1572874,2097162

%N 1/4 the number of (n+1) X 7 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.

%C Column 6 of A209727.

%H R. H. Hardin, <a href="/A209725/b209725.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*(12 + x - 23*x^2) / ((1 - x)*(1 - 2*x^2)).

%F a(n) = 3*2^(n/2 - 1) + 10 for n even.

%F a(n) = 2^((n + 1)/2) + 10 for n odd.

%F (End)

%e Some solutions for n=4:

%e ..1..0..1..0..1..0..1....2..0..2..0..1..0..2....0..1..0..1..0..1..0

%e ..0..2..0..2..0..2..0....1..2..1..2..0..2..1....2..0..2..0..2..0..2

%e ..1..0..1..0..1..0..1....2..0..2..0..1..0..2....0..1..0..1..0..1..0

%e ..0..2..0..2..0..2..0....1..2..1..2..0..2..1....2..0..2..0..2..0..2

%e ..1..0..1..0..1..0..1....2..0..2..0..1..0..2....0..1..0..1..0..1..0

%Y Cf. A209727.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 12 2012