%I #8 Aug 05 2018 08:21:43

%S 1,17,119,866,6328,46211,337274,2460918,17953576,130970758,955393448,

%T 6969190236,50836821440,370827923908,2704988609708,19731401249156,

%U 143929610463264,1049886222652688,7658333144969252,55863255070913284

%N Number of 2 X n arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, with no occupancy greater than 2.

%C Row 2 of A221328.

%H R. H. Hardin, <a href="/A221329/b221329.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 11*a(n-1) - 27*a(n-2) - a(n-3) + 8*a(n-4) - 16*a(n-5) - 6*a(n-6) + 2*a(n-7) for n>9.

%F Empirical g.f.: x*(1 + 6*x - 41*x^2 + 17*x^3 + 24*x^4 - 16*x^5 + x^6 + 5*x^7 - x^8) / (1 - 11*x + 27*x^2 + x^3 - 8*x^4 + 16*x^5 + 6*x^6 - 2*x^7). - _Colin Barker_, Aug 05 2018

%e Some solutions for n=3:

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

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

%Y Cf. A221328.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 11 2013