%I #8 Aug 05 2018 08:20:51

%S 0,4,10,29,84,242,696,2000,5744,16492,47344,135900,390080,1119636,

%T 3213616,9223756,26474016,75985524,218092816,625967180,1796642240,

%U 5156696372,14800673136,42480669068,121927372384,349954089588

%N Number of 2 X n arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, with every occupancy equal to zero or two.

%C Row 2 of A221419.

%H R. H. Hardin, <a href="/A221420/b221420.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x^2*(4 - 6*x + x^2 - 2*x^3 + x^4) / (1 - 4*x + 3*x^2 + 2*x^4). - _Colin Barker_, Aug 05 2018

%e Some solutions for n=3:

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

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

%Y Cf. A221419.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 15 2013