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%I #10 Oct 29 2023 02:30:42
%S 1,25,100,1089,6724,56644,400689,3122289,23049601,175350564,
%T 1311815961,9905822784,74413292944,560619075025,4216817073121,
%U 31746204178129,238880949939076,1798010762343849,13531178521076836,101839561889056996,766437062965271569
%N Number of n X 4 arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, with every occupancy equal to zero or two.
%H R. H. Hardin, <a href="/A221274/b221274.txt">Table of n, a(n) for n = 1..21</a>
%F Empirical: a(n) = 7*a(n-1) +16*a(n-2) -105*a(n-3) +108*a(n-4) +10*a(n-5) -56*a(n-6) -53*a(n-7) +23*a(n-8) -6*a(n-9) +a(n-10).
%e Some solutions for n=4:
%e ..0..2..2..0....0..2..2..0....0..0..2..2....0..0..2..0....2..2..2..0
%e ..2..0..0..0....2..0..0..2....2..2..0..0....0..2..2..2....0..2..0..2
%e ..0..2..2..0....2..2..0..2....0..0..2..2....2..0..2..2....0..0..2..0
%e ..0..2..2..2....0..0..2..0....0..2..2..0....0..2..0..0....2..2..0..0
%Y Column 4 of A221275.
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 09 2013