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%I #5 Jan 24 2013 07:27:08
%S 1,19,98,817,5567,41067,293058,2119375,15244204,109884658,791399401,
%T 5701648165,41072174493,295881007510,2131463579726,15354723297804,
%U 110612658781667,796834506416273,5740255973053614,41351802973320254
%N Number of nX2 arrays of occupancy after each element moves to some king-move neighbor, without move-in move-out straight through or left turns
%C Column 2 of A221749
%H R. H. Hardin, <a href="/A221746/b221746.txt">Table of n, a(n) for n = 1..59</a>
%F Empirical: a(n) = 3*a(n-1) +33*a(n-2) +7*a(n-3) -165*a(n-4) -152*a(n-5) -189*a(n-6) -572*a(n-7) -280*a(n-8) -223*a(n-9) -745*a(n-10) -574*a(n-11) -882*a(n-12) -773*a(n-13) -298*a(n-14) -128*a(n-15) +4*a(n-16) +19*a(n-17) +3*a(n-18)
%e Some solutions for n=3
%e ..2..1....0..3....0..2....2..1....1..2....2..0....0..2....0..1....0..1....1..0
%e ..1..0....0..1....1..2....1..0....2..1....1..1....3..1....3..1....1..1....2..1
%e ..2..0....1..1....0..1....1..1....0..0....1..1....0..0....0..1....3..0....1..1
%K nonn
%O 1,2
%A _R. H. Hardin_ Jan 24 2013