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A233129 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs) 8

%I

%S 1,1,1,3,8,3,10,80,80,10,36,896,2688,896,36,136,10496,96256,96256,

%T 10496,136,528,124928,3497984,10674176,3497984,124928,528,2080,

%U 1495040,127533056,1189609472,1189609472,127533056,1495040,2080,8256,17924096

%N T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs)

%C Table starts

%C .....1..........1...............3...................10

%C .....1..........8..............80..................896

%C .....3.........80............2688................96256

%C ....10........896...........96256.............10674176

%C ....36......10496.........3497984...........1189609472

%C ...136.....124928.......127533056.........132682612736

%C ...528....1495040......4653056000.......14800557965312

%C ..2080...17924096....169793814528.....1651015493353472

%C ..8256..215023616...6196127858688...184172904936636416

%C .32896.2580021248.226111237652480.20544737466392772608

%H R. H. Hardin, <a href="/A233129/b233129.txt">Table of n, a(n) for n = 1..364</a>

%F Empirical for column k:

%F k=1: a(n) = 6*a(n-1) -8*a(n-2) for n>3

%F k=2: a(n) = 16*a(n-1) -48*a(n-2)

%F k=3: a(n) = 48*a(n-1) -448*a(n-2) +1024*a(n-3)

%F k=4: a(n) = 160*a(n-1) -6144*a(n-2) +86016*a(n-3) -393216*a(n-4)

%F k=5: [order 6]

%F k=6: [order 8]

%F k=7: [order 14]

%F Empirical for row n:

%F n=1: a(n) = 6*a(n-1) -8*a(n-2) for n>3

%F n=2: a(n) = 16*a(n-1) -48*a(n-2)

%F n=3: a(n) = 48*a(n-1) -448*a(n-2) +1024*a(n-3)

%F n=4: a(n) = 160*a(n-1) -6144*a(n-2) +86016*a(n-3) -393216*a(n-4)

%F n=5: [order 6]

%F n=6: [order 8]

%F n=7: [order 14]

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A007582(n-2)

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Dec 04 2013

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Last modified July 28 19:33 EDT 2021. Contains 346335 sequences. (Running on oeis4.)