%I #7 Mar 31 2012 12:37:31

%S 2799,95830,3125615,102841182,3382058727,111283430198,3662188386511,

%T 120530162560270,3967087049431415,130574878781163590,

%U 4297873984238326975,141465674364112336606,4656399600486593129991,153267603929372883975350

%N Number of (n+1)X6 0..2 arrays with every 2X2 subblock having one or three distinct values, and new values 0..2 introduced in row major order

%C Column 5 of A210107

%H R. H. Hardin, <a href="/A210104/b210104.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 68*a(n-1) -1109*a(n-2) -15132*a(n-3) +533650*a(n-4) -682812*a(n-5) -91388848*a(n-6) +541468084*a(n-7) +8010220974*a(n-8) -76037057944*a(n-9) -380609964150*a(n-10) +5713624684772*a(n-11) +7546313419928*a(n-12) -272240689140684*a(n-13) +185952132990252*a(n-14) +8790130916081940*a(n-15) -18031849778390353*a(n-16) -197980986867193344*a(n-17) +636160628144662267*a(n-18) +3122695677229408840*a(n-19) -14015802619871969522*a(n-20) -33484157496106096408*a(n-21) +214830105901029340796*a(n-22) +215490176857593683592*a(n-23) -2386196515012527746772*a(n-24) -278928178726785919580*a(n-25) +19547830951977668052136*a(n-26) -10058031406426519679456*a(n-27) -118783413433906506268928*a(n-28) +120366274979665650042448*a(n-29) +533880171597066533206896*a(n-30) -778900186987919254121344*a(n-31) -1754277169343190873917504*a(n-32) +3380528371752993713671808*a(n-33) +4110607686089791274598592*a(n-34) -10417505934114336408844032*a(n-35) -6508643137572987893783936*a(n-36) +23248657105901998508654080*a(n-37) +5969723267297107040175616*a(n-38) -37777911031496989203732480*a(n-39) -751674288908450157042688*a(n-40) +44600619081046898666690560*a(n-41) -5794844778782401587208192*a(n-42) -37966938282556065993916416*a(n-43) +8160526737847235042664448*a(n-44) +23005895699982159363768320*a(n-45) -5661409259903212447334400*a(n-46) -9727195323636513269350400*a(n-47) +2227995919449608334737408*a(n-48) +2777538507080041554247680*a(n-49) -472156158151071247630336*a(n-50) -504235867339370029645824*a(n-51) +41294805044945664081920*a(n-52) +51365990278841539493888*a(n-53) +588902075096209817600*a(n-54) -2181425252011962531840*a(n-55) -163298906545663770624*a(n-56) +18362493445475401728*a(n-57) +1626733500608544768*a(n-58)

%e Some solutions for n=4

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 17 2012