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Number of 3 X n arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.
1

%I #7 Aug 10 2018 17:34:03

%S 0,4,0,43,44,736,1680,14548,47314,307629,1201506,6768794,29159864,

%T 152481584,692301668,3481342319,16253985408,80073291120,379418253880,

%U 1849109113064,8830193356854,42791854403241,205182113819686

%N Number of 3 X n arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.

%C Row 3 of A221755.

%H R. H. Hardin, <a href="/A221757/b221757.txt">Table of n, a(n) for n = 1..73</a>

%F Empirical: a(n) = 27*a(n-2) + 14*a(n-3) - 165*a(n-4) - 20*a(n-5) + 329*a(n-6) - 48*a(n-7) - 131*a(n-8) - 34*a(n-9) + 9*a(n-10).

%F Empirical g.f.: x^2*(4 - 65*x^2 - 12*x^3 + 235*x^4 - 30*x^5 - 161*x^6 - 38*x^7 + 10*x^8) / (1 - 27*x^2 - 14*x^3 + 165*x^4 + 20*x^5 - 329*x^6 + 48*x^7 + 131*x^8 + 34*x^9 - 9*x^10). - _Colin Barker_, Aug 10 2018

%e Some solutions for n=4:

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

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

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

%Y Cf. A221755.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 24 2013