%I #9 Aug 15 2018 12:38:39

%S 1,5,17,53,159,467,1356,3913,11253,32299,92606,265353,760080,2176758,

%T 6233232,17847997,51103477,146319703,418938535,1199485661,3434300229,

%U 9832876386,28152852451,80605364957,230783807849,660764392260

%N Number of (n+2) X 1 arrays of occupancy after each element moves up to +-2 places but not 0 and without 2-loops.

%C Column 2 of A222165.

%H R. H. Hardin, <a href="/A222160/b222160.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + a(n-2) - 3*a(n-3) - 2*a(n-4) - 2*a(n-5) - a(n-6).

%F Empirical g.f.: x*(1 + x)^2 / ((1 - x - x^2)*(1 - 2*x - 2*x^2 - x^3 - x^4)). - _Colin Barker_, Aug 15 2018

%e Some solutions for n=3:

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

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

%e ..3....1....2....3....1....1....2....1....2....3....2....1....2....1....2....2

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

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

%Y Cf. A222165.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 10 2013