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%I #4 Jan 05 2013 08:22:07
%S 2,119,2372,54075,1211716,27341781,616856209,13916105891,313875248748,
%T 7078358754222,159612315673169,3598939207596752,81145945154370610,
%U 1829571759949287263,41250206743699390677,930034721423526268618
%N Number of nX3 arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, with no occupancy greater than 2
%C Column 3 of A221234
%H R. H. Hardin, <a href="/A221231/b221231.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 59*a(n-1) -1318*a(n-2) +14092*a(n-3) -67451*a(n-4) -20429*a(n-5) +1690470*a(n-6) -5449489*a(n-7) -11413301*a(n-8) +92565730*a(n-9) -9734325*a(n-10) -961575028*a(n-11) +1183796707*a(n-12) +7379548273*a(n-13) -18061070430*a(n-14) -34705198474*a(n-15) +158971932525*a(n-16) +55660862589*a(n-17) -982167551757*a(n-18) +577010582103*a(n-19) +4720057513407*a(n-20) -7161970921834*a(n-21) -15215640411402*a(n-22) +43223451073762*a(n-23) +18014445056311*a(n-24) -149972209079997*a(n-25) +58768499243289*a(n-26) +309896713124274*a(n-27) -279346283283773*a(n-28) -419213503384717*a(n-29) +578203122451758*a(n-30) +418750718477635*a(n-31) -866232445035235*a(n-32) -207819360413378*a(n-33) +939644214006037*a(n-34) -202156347964894*a(n-35) -529157887538075*a(n-36) +342187678823239*a(n-37) +6924219360478*a(n-38) -93047297947560*a(n-39) +111057043021023*a(n-40) -72770035832361*a(n-41) -21062410675835*a(n-42) +47703159259219*a(n-43) -9997858341151*a(n-44) -10643592144074*a(n-45) +4709985828030*a(n-46) +1032138628992*a(n-47) -868291263418*a(n-48) -5308241010*a(n-49) +88268192081*a(n-50) -9040938180*a(n-51) -5100948232*a(n-52) +936681530*a(n-53) +145155840*a(n-54) -41898204*a(n-55) -594108*a(n-56) +746320*a(n-57) -45456*a(n-58)
%e Some solutions for n=3
%e ..0..2..1....0..2..0....0..0..0....0..2..0....1..1..0....1..0..2....0..0..0
%e ..2..1..0....1..2..2....2..1..0....0..2..2....0..2..1....1..2..1....2..2..1
%e ..1..2..0....1..0..1....2..2..2....0..2..1....0..2..2....0..1..1....1..1..2
%K nonn
%O 1,1
%A _R. H. Hardin_ Jan 05 2013
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