%I #9 Feb 05 2019 18:42:35

%S 5,11,45,173,693,2765,11061,44237,176949,707789,2831157,11324621,

%T 45298485,181193933,724775733,2899102925,11596411701,46385646797,

%U 185542587189,742170348749,2968681394997,11874725579981,47498902319925

%N Number of 3 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,1) or (0,-1) and new values introduced in order 0..2.

%H R. H. Hardin, <a href="/A276300/b276300.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + a(n-2) - 4*a(n-3) for n>4.

%F Conjectures from _Colin Barker_, Feb 05 2019: (Start)

%F G.f.: x*(5 - 9*x - 4*x^2 + 2*x^3) / ((1 - x)*(1 + x)*(1 - 4*x)).

%F a(n) = (8 + 27*4^n) / 40 for n>1 and even.

%F a(n) = (72 + 27*4^n) / 40 for n>1 and odd.

%F (End)

%e Some solutions for n=4:

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

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

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

%Y Row 3 of A276299.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 28 2016