A221883 - OEIS

%I #9 Aug 11 2018 10:45:53

%S 3,33,326,3223,31832,314426,3105733,30676867,303010527,2992984402,

%T 29563182686,292010132356,2884328060800,28489930453209,

%U 281409090823688,2779616346494657,27455641219994600,271192906082774221

%N Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without consecutive moves in the same direction.

%C Column 2 of A221886.

%H R. H. Hardin, <a href="/A221883/b221883.txt">Table of n, a(n) for n = 1..55</a>

%F Empirical: a(n) = 7*a(n-1) + 27*a(n-2) + 16*a(n-3) - 18*a(n-4) - 13*a(n-5) + 5*a(n-6) + 3*a(n-7) - a(n-8).

%F Empirical g.f.: x*(3 + 12*x + 14*x^2 + 2*x^3 - 5*x^4 - 2*x^5 + x^6) / (1 - 7*x - 27*x^2 - 16*x^3 + 18*x^4 + 13*x^5 - 5*x^6 - 3*x^7 + x^8). - _Colin Barker_, Aug 11 2018

%e Some solutions for n=3:

%e ..1..2....0..3....0..3....0..2....1..0....0..1....1..1....1..1....1..0....0..1

%e ..0..0....0..1....0..3....0..2....1..1....2..0....0..2....1..0....3..1....3..1

%e ..0..3....0..2....0..0....2..0....1..2....0..3....0..2....0..3....1..0....0..1

%Y Cf. A221886.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 30 2013