%I #6 Jun 07 2023 20:13:54
%S 13,783,36467,1759041,84547866,4065176472,195452177326,9397301189681,
%T 451820171352622,21723415149940892,1044457051240660759,
%U 50217266705524767168,2414435205611270005630,116085516886164224493024
%N Number of n X 4 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.
%C Column 4 of A221937.
%H R. H. Hardin, <a href="/A221934/b221934.txt">Table of n, a(n) for n = 1..157</a>
%F Empirical: a(n) = 45*a(n-1) +166*a(n-2) -812*a(n-3) -2452*a(n-4) +2243*a(n-5) +23138*a(n-6) +2192*a(n-7) +908*a(n-8) +6885*a(n-9) -5028*a(n-10) +3940*a(n-11) -628*a(n-12) +36*a(n-13).
%e Some solutions for n=3
%e ..1..3..0..1....0..1..0..0....1..1..2..1....1..3..0..0....1..0..0..2
%e ..0..2..1..0....3..1..2..2....0..0..2..2....0..0..3..2....2..2..1..0
%e ..0..1..2..1....1..1..1..0....2..0..0..1....1..1..1..0....0..2..2..0
%Y Cf. A221937.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 01 2013