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

%I #7 Feb 04 2019 09:08:31

%S 3,16,84,444,2344,12376,65344,345008,1821600,9617824,50780928,

%T 268117056,1415625088,7474326400,39463524352,208362556160,

%U 1100128676352,5808544139776,30668398841856,161925374911488,854946069256192

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

%H R. H. Hardin, <a href="/A275402/b275402.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 6*a(n-2) + 4*a(n-3).

%F Empirical g.f.: x*(3 + 4*x + 2*x^2) / (1 - 4*x - 6*x^2 - 4*x^3). - _Colin Barker_, Feb 04 2019

%e Some solutions for n=4:

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

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

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

%Y Row 3 of A275401.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jul 26 2016