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A221829 Number of 2 X n arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

%I A221829 #12 Aug 11 2018 10:45:49
%S A221829 0,3,16,73,333,1519,6929,31607,144177,657671,3000001,13684663,
%T A221829 62423313,284747239,1298889569,5924953367,27026987697,123285031751,
%U A221829 562371183361,2565285853303,11701686899793,53377862792359,243485940162209
%N A221829 Number of 2 X n arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.
%C A221829 Row 2 of A221828.
%H A221829 R. H. Hardin, <a href="/A221829/b221829.txt">Table of n, a(n) for n = 1..210</a>
%F A221829 Empirical: a(n) = 5*a(n-1) - 2*a(n-2) for n>4.
%F A221829 Conjectures from _Colin Barker_, Aug 11 2018: (Start)
%F A221829 G.f.: x^2*(3 + x - x^2) / (1 - 5*x + 2*x^2).
%F A221829 a(n) = (2^(-4-n)*((5-sqrt(17))^n*(-7+sqrt(17)) + (5+sqrt(17))^n*(7+sqrt(17)))) / sqrt(17) for n>2.
%F A221829 (End)
%e A221829 Some solutions for n=3:
%e A221829 ..1..1..0....0..2..0....0..2..1....0..2..1....1..1..1....0..2..2....1..1..0
%e A221829 ..2..1..1....1..2..1....1..2..0....1..1..1....1..2..0....0..1..1....1..2..1
%Y A221829 Cf. A221828.
%K A221829 nonn
%O A221829 1,2
%A A221829 _R. H. Hardin_, Jan 26 2013