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A205349 Number of (n+1)X4 0..3 arrays with no 2X2 subblock having the same number of equal edges as its horizontal or vertical neighbors, and new values 0..3 introduced in row major order 1

%I

%S 1024,30904,1080457,36759026,1257218433,43053361050,1474675468656,

%T 50476796838096,1729398847976636,59200115247949262,

%U 2028085463265593293,69429755260198744630,2378394585304190653410,81426385042606078434044

%N Number of (n+1)X4 0..3 arrays with no 2X2 subblock having the same number of equal edges as its horizontal or vertical neighbors, and new values 0..3 introduced in row major order

%C Column 3 of A205352

%H R. H. Hardin, <a href="/A205349/b205349.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 1314*a(n-2) +1004*a(n-3) -254046*a(n-4) +1403430*a(n-5) +20011065*a(n-6) -71345248*a(n-7) -3853281227*a(n-8) +24166488912*a(n-9) +115376085119*a(n-10) -1583603564624*a(n-11) +285661767186*a(n-12) +49049732128358*a(n-13) -228955111284505*a(n-14) +902395229430644*a(n-15) -7109329681528133*a(n-16) +49595269396263970*a(n-17) -462419264290913651*a(n-18) +2337355241735241460*a(n-19) +4209648146017411480*a(n-20) -59956332667716770644*a(n-21) +164935592319417959956*a(n-22) -618493486063622677780*a(n-23) +3305743223212436966137*a(n-24) +364227432914454495246*a(n-25) +104832075525022939045750*a(n-26) -658041570619001734722264*a(n-27) -779825962384733258766876*a(n-28) +9352928393327167881935192*a(n-29) -27623158603287845487677464*a(n-30) +184369296373835759421876536*a(n-31) -345268461461300829263246048*a(n-32) -1433859802472779572432687664*a(n-33) +1244074747434809920123909920*a(n-34) +12788632703808413378747343040*a(n-35) -8403311148747530107603755520*a(n-36) +28843585714409912694578390144*a(n-37) -265924423127031646657646012928*a(n-38) +95844993201302765140262692864*a(n-39) +897775279837025840435150438400*a(n-40) -473146805523880610077036494848*a(n-41) -1734935554775363726435805224960*a(n-42) +839692297306925187134268612608*a(n-43) +7430741769362028910355035029504*a(n-44) +4600782608235370499293043523584*a(n-45) -30153711437470808965174721249280*a(n-46) -67619065507298070156314571046912*a(n-47) +128419240847963530835141597855744*a(n-48) +259960937077059172579928072781824*a(n-49) -549200407626519006722621435805696*a(n-50) -383758536010056191881054756274176*a(n-51) +1306416786679990434306297511804928*a(n-52) -60430476997171629616472281579520*a(n-53) -1145480954211698647652944547151872*a(n-54) +615780543160777621646069800632320*a(n-55) -104484250012188123195917578797056*a(n-56) -354990146445320200920379443642368*a(n-57) +508655587529402937037917024944128*a(n-58) -167135243612198795923575585898496*a(n-59) +5842822885925355807358410817536*a(n-60) +35770461876486362152428103532544*a(n-61) -33703813612879839814679556784128*a(n-62) +1942541055161343649385948381184*a(n-63) +2423993898978467194990032322560*a(n-64) for n>65

%e Some solutions for n=4

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

%e ..0..2..1..1....1..0..2..1....0..0..1..2....2..1..2..3....0..1..0..0

%e ..0..1..3..2....3..3..0..0....3..3..1..1....0..3..2..2....1..2..0..0

%e ..3..0..3..2....1..3..2..2....0..1..2..3....1..3..2..2....3..2..2..1

%e ..1..0..3..0....2..2..3..0....2..3..3..0....0..1..1..2....1..3..1..1

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 26 2012

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Last modified February 2 23:07 EST 2023. Contains 360024 sequences. (Running on oeis4.)