%I #10 Jan 31 2019 19:36:41
%S 4,48,224,1088,5248,25344,122368,590848,2852864,13774848,66510848,
%T 321142784,1550614528,7487029248,36150575104,174550417408,
%U 842803970048,4069417549824,19648886079488,94873214517248,458088402386944
%N Number of n X 4 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,-2) or (0,-1) and new values introduced in order 0..2.
%H R. H. Hardin, <a href="/A275138/b275138.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) + 4*a(n-2) for n>3.
%F Conjectures from _Colin Barker_, Jan 31 2019: (Start)
%F G.f.: 4*x*(1 + 8*x + 4*x^2) / (1 - 4*x - 4*x^2).
%F a(n) = 2*((2-2*sqrt(2))^n + (2*(1+sqrt(2)))^n) for n>1.
%F (End)
%e Some solutions for n=5:
%e ..0..1..2..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..2..0
%e ..2..0..1..2. .0..2..1..0. .0..1..2..0. .2..1..2..0. .2..1..2..0
%e ..1..2..1..2. .1..0..2..0. .1..2..1..2. .2..0..1..2. .1..0..1..0
%e ..0..2..0..1. .1..0..2..1. .1..0..2..0. .0..1..0..2. .0..2..0..2
%e ..1..0..2..0. .2..1..0..2. .2..1..0..1. .1..2..1..2. .2..1..2..1
%Y Column 4 of A275142.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jul 17 2016