A241073 - OEIS

%I #10 Oct 29 2018 10:18:43

%S 1,4,12,39,131,444,1516,5195,17847,61424,211672,730119,2520091,

%T 8702628,30063396,103881123,359017439,1240945016,4289745552,

%U 14829991071,51271047939,177263517036,612883590684,2119068084731,7326858673287

%N Number of n X 2 0..2 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..2 introduced in row major order.

%H R. H. Hardin, <a href="/A241073/b241073.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 8*a(n-2) - 4*a(n-3) + a(n-4) + 14*a(n-5) - 8*a(n-6) for n>7.

%F Empirical g.f.: x*(1 + x)*(1 - 3*x - x^2 + 4*x^3 + 4*x^4 - 4*x^5) / ((1 - x)*(1 - 5*x + 3*x^2 + 7*x^3 + 6*x^4 - 8*x^5)). - _Colin Barker_, Oct 29 2018

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A241078.

%K nonn

%O 1,2

%A _R. H. Hardin_, Apr 15 2014