A230269 - OEIS

A230269

Number of n X 2 0..2 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

%I #8 Feb 24 2018 07:50:38

%S 0,0,2,8,30,108,386,1376,4902,17460,62186,221480,788814,2809404,

%T 10005842,35636336,126920694,452034756,1609945658,5733906488,

%U 20421610782,72732645324,259041157538,922588763264,3285848604870,11702723341140

%N Number of n X 2 0..2 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

%C Column 2 of A230275.

%H R. H. Hardin, <a href="/A230269/b230269.txt">Table of n, a(n) for n = 1..210</a>

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

%F Conjectures from _Colin Barker_, Feb 24 2018: (Start)

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

%F a(n) = -1/2 + (2^(-2-n)*(-(-5+sqrt(17))*(3+sqrt(17))^n - (3-sqrt(17))^n*(5+sqrt(17)))) / sqrt(17).

%F (End)

%e All solutions for n=3:

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

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

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

%Y Cf. A230275.

%K nonn

%O 1,3

%A _R. H. Hardin_, Oct 14 2013