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A221731 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.

%I A221731 #8 Mar 14 2018 11:05:20
%S A221731 3,17,91,489,2627,14113,75819,407321,2188243,11755857,63155771,
%T A221731 339290569,1822764387,9792403073,52607544139,282622526841,
%U A221731 1518327722483,8156883666097,43821073775451,235419136209449,1264737828598147
%N A221731 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 A221731 Column 2 of A221736.
%H A221731 R. H. Hardin, <a href="/A221731/b221731.txt">Table of n, a(n) for n = 1..210</a>
%F A221731 Empirical: a(n) = 5*a(n-1) + 2*a(n-2).
%F A221731 Conjectures from _Colin Barker_, Mar 14 2018: (Start)
%F A221731 G.f.: x*(3 + 2*x) / (1 - 5*x - 2*x^2).
%F A221731 a(n) = (2^(-1-n)*((5-sqrt(33))^n*(-1+sqrt(33)) + (1+sqrt(33))*(5+sqrt(33))^n)) / sqrt(33).
%F A221731 (End)
%e A221731 Some solutions for n=3:
%e A221731 ..2..0....1..0....1..0....0..2....0..2....0..2....2..0....1..1....1..0....2..0
%e A221731 ..2..0....3..0....3..0....2..0....1..2....0..2....1..1....2..0....2..2....0..1
%e A221731 ..0..2....1..1....0..2....2..0....0..1....2..0....2..0....0..2....0..1....2..1
%Y A221731 Cf. A221736.
%K A221731 nonn
%O A221731 1,1
%A A221731 _R. H. Hardin_, Jan 22 2013