A204534 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

660, 9043, 132993, 1303179, 16041873, 207574351, 2345643287, 28467730050, 350678109167, 4126222857239, 49819224759981, 603924610295384, 7206803236762964, 86812811732551040, 1046777031811904138

Offset

1,1

Comments

Column 1 of A204538

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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)

Example

Some solutions for n=3
..0..0..0....0..0..0....0..0..0....0..0..0....0..1..0....0..1..2....0..0..0
..1..1..1....1..0..1....1..0..1....0..0..0....0..1..0....2..3..2....1..1..0
..1..2..1....0..0..1....2..1..0....1..2..3....0..1..1....2..2..2....1..1..0
..2..3..1....1..0..1....1..1..1....2..2..2....0..0..0....2..0..0....2..1..0
..1..1..1....0..0..1....0..0..0....2..2..1....0..1..1....1..1..1....0..0..0

Crossrefs

Sequence in context: A064261 A235770 A204538 * A235553 A342994 A252457

Adjacent sequences: A204531 A204532 A204533 * A204535 A204536 A204537

Keyword

nonn

Author

R. H. Hardin Jan 16 2012

Status

approved