A221731 - OEIS

%I #8 Mar 14 2018 11:05:20

%S 3,17,91,489,2627,14113,75819,407321,2188243,11755857,63155771,

%T 339290569,1822764387,9792403073,52607544139,282622526841,

%U 1518327722483,8156883666097,43821073775451,235419136209449,1264737828598147

%N Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out left turns.

%C Column 2 of A221736.

%H R. H. Hardin, <a href="/A221731/b221731.txt">Table of n, a(n) for n = 1..210</a>

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

%F Conjectures from _Colin Barker_, Mar 14 2018: (Start)

%F G.f.: x*(3 + 2*x) / (1 - 5*x - 2*x^2).

%F a(n) = (2^(-1-n)*((5-sqrt(33))^n*(-1+sqrt(33)) + (1+sqrt(33))*(5+sqrt(33))^n)) / sqrt(33).

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A221736.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 22 2013