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%I #4 Jan 12 2013 06:52:50
%S 0,39,791,18738,410571,9021576,197291655,4313255090,94259266376,
%T 2059682765099,45003771497723,983297420299208,21483920167245180,
%U 469394579747198225,10255579972679828734,224068598231298074183
%N Number of nX3 arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, with no 2-loops and with no occupancy greater than 2
%C Column 3 of A221361
%H R. H. Hardin, <a href="/A221358/b221358.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 55*a(n-1) -1084*a(n-2) +8549*a(n-3) -1355*a(n-4) -385061*a(n-5) +1800306*a(n-6) +3048157*a(n-7) -40693450*a(n-8) +40463509*a(n-9) +389976177*a(n-10) -915210221*a(n-11) -1594990966*a(n-12) +6521378910*a(n-13) +1099516549*a(n-14) -21384055027*a(n-15) +9995004390*a(n-16) +30116092385*a(n-17) -19117627065*a(n-18) -8399838021*a(n-19) -33520539625*a(n-20) +22367240257*a(n-21) +129769144158*a(n-22) -170325950186*a(n-23) -105655501048*a(n-24) +272513454532*a(n-25) +39549648231*a(n-26) -109801210903*a(n-27) -258303659042*a(n-28) +22269528983*a(n-29) +541846105860*a(n-30) -324496641619*a(n-31) -396262749420*a(n-32) +542792407937*a(n-33) +80707793127*a(n-34) -350739533054*a(n-35) +5434124804*a(n-36) +93044173858*a(n-37) +37885776912*a(n-38) -21512214212*a(n-39) -16893408979*a(n-40) -4605082277*a(n-41) +11255360114*a(n-42) -295280483*a(n-43) -3316068231*a(n-44) +859574403*a(n-45) +6641752*a(n-46) -48057886*a(n-47) -11472068*a(n-48) -580856*a(n-49) +1360*a(n-50) for n>52
%e Some solutions for n=3
%e ..1..1..1....1..1..0....0..2..1....1..2..1....1..1..1....1..0..0....1..2..1
%e ..1..0..2....2..2..2....1..0..2....1..2..2....1..0..1....1..2..1....1..2..1
%e ..0..2..1....1..0..0....0..2..1....0..0..0....2..1..1....2..2..0....1..0..0
%K nonn
%O 1,2
%A _R. H. Hardin_ Jan 12 2013
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