A253029 - OEIS

%I #9 Dec 08 2018 11:22:29

%S 297,1647,9126,50571,280233,1552878,8605089,47684079,264235662,

%T 1464230547,8113859721,44961990246,249151530393,1380643622703,

%U 7650672704694,42395294391579,234928490071977,1301828333534622

%N Number of (n+2) X (1+2) 0..2 arrays with every consecutive three elements in every row and column having exactly two distinct values, and new values 0 upwards introduced in row major order.

%H R. H. Hardin, <a href="/A253029/b253029.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) + 3*a(n-2).

%F Conjectures from _Colin Barker_, Dec 08 2018: (Start)

%F G.f.: 27*x*(11 + 6*x) / (1 - 5*x - 3*x^2).

%F a(n) = (27*2^(-n)*((5-sqrt(37))^n*(-6+sqrt(37)) + (5+sqrt(37))^n*(6+sqrt(37)))) / sqrt(37).

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 1 of A253035.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 26 2014