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%I #6 Mar 31 2012 12:37:02
%S 660,9043,132993,1303179,16041873,207574351,2345643287,28467730050,
%T 350678109167,4126222857239,49819224759981,603924610295384,
%U 7206803236762964,86812811732551040,1046777031811904138
%N Number of (n+2)X3 0..3 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly two ways, and new values 0..3 introduced in row major order
%C Column 1 of A204538
%H R. H. Hardin, <a href="/A204534/b204534.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 9*a(n-1) +8*a(n-2) +923*a(n-3) -6342*a(n-4) -939*a(n-5) -173958*a(n-6) +901943*a(n-7) +2062525*a(n-8) +8902462*a(n-9) -48780449*a(n-10) -282124297*a(n-11) -166932728*a(n-12) +2115174147*a(n-13) +11504924005*a(n-14) +10153975068*a(n-15) -69498155436*a(n-16) -209730402340*a(n-17) -406440518622*a(n-18) -16788307886*a(n-19) +3659177431184*a(n-20) +10384002709932*a(n-21) +16242854423036*a(n-22) +2093722285538*a(n-23) -106528521998844*a(n-24) -432747452598976*a(n-25) -882991567703989*a(n-26) -259277064737291*a(n-27) +3679442805829471*a(n-28) +12444453117538998*a(n-29) +23785684974440218*a(n-30) +19887533685435438*a(n-31) -58900715496361184*a(n-32) -302384413595569938*a(n-33) -609659015783024124*a(n-34) -311034592306197668*a(n-35) +1592055595808779794*a(n-36) +4685425755299850878*a(n-37) +5255152773407570353*a(n-38) -1517381330117066715*a(n-39) -14399294037197206623*a(n-40) -22609895601580348062*a(n-41) -16046297784101517372*a(n-42) -334366805037484800*a(n-43) +8481694658635279656*a(n-44) +10924616332492918380*a(n-45) +31692272997322138491*a(n-46) +80201258825777560161*a(n-47) +114427329286469792094*a(n-48) +78467092131372656985*a(n-49) -17737148077455158136*a(n-50) -93441798420479428581*a(n-51) -89955562564618340328*a(n-52) -27239859385189557471*a(n-53) +58493487837118185549*a(n-54) +174223181810771175798*a(n-55) +303585517554413607018*a(n-56) +334169263667192519502*a(n-57) +160766147475245524464*a(n-58) -138222825173863341516*a(n-59) -337282784922743738028*a(n-60) -304497896419523223864*a(n-61) -133512338618439563448*a(n-62) -2398598016064323624*a(n-63) +23606203138568253504*a(n-64) +618197539013197056*a(n-65) -8635084684523203968*a(n-66) -2725837499493826560*a(n-67) +28920784535654400*a(n-68)
%e Some solutions for n=3
%e ..0..0..0....0..0..0....0..0..0....0..0..0....0..1..0....0..1..2....0..0..0
%e ..1..1..1....1..0..1....1..0..1....0..0..0....0..1..0....2..3..2....1..1..0
%e ..1..2..1....0..0..1....2..1..0....1..2..3....0..1..1....2..2..2....1..1..0
%e ..2..3..1....1..0..1....1..1..1....2..2..2....0..0..0....2..0..0....2..1..0
%e ..1..1..1....0..0..1....0..0..0....2..2..1....0..1..1....1..1..1....0..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Jan 16 2012
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