%I #5 Mar 31 2012 12:35:52

%S 4,36,256,2088,16512,131072,1048576,8392704,67113216,536870912,

%T 4295098368,34359738368,274877906944,2199028248576,17592186044416,

%U 140737488355328,1125900041060352,9007199254740992,72057594105298944

%N Half the number of nX3 0..2 arrays with no element equal to the sum mod 3 of its horizontal and vertical neighbors

%C Column 3 of A183501

%H R. H. Hardin, <a href="/A183496/b183496.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n)=8*a(n-1)+32*a(n-3)-256*a(n-4)+160*a(n-5)-1280*a(n-6)-5120*a(n-8)+40960*a(n-9)-4096*a(n-10)+32768*a(n-11)+131072*a(n-13)-1048576*a(n-14)+532480*a(n-15)-4259840*a(n-16)-17039360*a(n-18)+136314880*a(n-19)-85196800*a(n-20)+681574400*a(n-21)+2726297600*a(n-23)-21810380800*a(n-24)+2181038080*a(n-25)-17448304640*a(n-26)-69793218560*a(n-28)+558345748480*a(n-29)-4294967296*a(n-30)+34359738368*a(n-31)+137438953472*a(n-33)-1099511627776*a(n-34)+687194767360*a(n-35)-5497558138880*a(n-36)-21990232555520*a(n-38)+175921860444160*a(n-39)-17592186044416*a(n-40)+140737488355328*a(n-41)+562949953421312*a(n-43)-4503599627370496*a(n-44)

%e Some solutions for 5X3

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 05 2011