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Number of 2 X n arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, without move-in move-out straight through or left turns.
1

%I #6 May 20 2023 07:59:47

%S 0,4,16,91,459,2429,12678,66380,347305,1817234,9509123,49756006,

%T 260353922,1362310931,7128385902,37299670925,195172780250,

%U 1021252966367,5343766480365,27961572573739,146310575925354,765578706008096

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

%H R. H. Hardin, <a href="/A221818/b221818.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +17*a(n-2) +25*a(n-3) +7*a(n-4) +15*a(n-5) +10*a(n-6) -19*a(n-7) +8*a(n-8) +9*a(n-9) +2*a(n-10) -3*a(n-11) +a(n-12).

%e Some solutions for n=3

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

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

%Y Row 2 of A221817.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 26 2013