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T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order
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%I #4 Dec 06 2013 06:12:10

%S 1,2,2,6,14,6,23,174,174,23,99,2541,8231,2541,99,452,39203,420948,

%T 420948,39203,452,2136,616454,21895530,72049266,21895530,616454,2136,

%U 10313,9757236,1142726121,12389989684,12389989684,1142726121,9757236,10313

%N T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order

%C Table starts

%C ......1...........2................6.....................23

%C ......2..........14..............174...................2541

%C ......6.........174.............8231.................420948

%C .....23........2541...........420948...............72049266

%C .....99.......39203.........21895530............12389989684

%C ....452......616454.......1142726121..........2131764323784

%C ...2136.....9757236......59679029456........366805442634477

%C ..10313...154782591....3117164734533......63115455429961173

%C ..50469..2457231917..162820623245643...10860156414181066717

%C .249062.39019481264.8504746957840386.1868686679256045815893

%H R. H. Hardin, <a href="/A233230/b233230.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

%F k=1: a(n) = 9*a(n-1) -23*a(n-2) +15*a(n-3)

%F k=2: a(n) = 21*a(n-1) -79*a(n-2) -41*a(n-3) +72*a(n-4) +28*a(n-5)

%F k=3: [order 10]

%F k=4: [order 23]

%e Some solutions for n=3 k=4

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

%e ..1..0..2..5....3..0..1..1....1..0..2..2....1..0..2..4....0..0..2..2

%e ..1..0..1..1....3..0..2..5....1..1..1..1....1..2..4..5....0..1..1..0

%Y Column 1 is A233106

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Dec 06 2013