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T(n,k)=Number of 0..4 colorings of an nx(k+1) array circular in the k+1 direction with new values 0..4 introduced in row major order
14

%I #4 Jul 05 2012 06:18:25

%S 1,1,4,4,17,33,11,257,514,380,40,3074,28278,16388,4801,147,40434,

%T 1101051,3221873,524296,62004,568,522515,47730973,396246659,367793014,

%U 16777232,804833,2227,6800539,2000093424,56449101747,142612676441,41989913081

%N T(n,k)=Number of 0..4 colorings of an nx(k+1) array circular in the k+1 direction with new values 0..4 introduced in row major order

%C Table starts

%C ....1......1.........4...........11.............40...............147

%C ....4.....17.......257.........3074..........40434............522515

%C ...33....514.....28278......1101051.......47730973........2000093424

%C ..380..16388...3221873....396246659....56449101747.....7658621867351

%C .4801.524296.367793014.142612676441.66761857485037.29325981412599886

%H R. H. Hardin, <a href="/A214141/b214141.txt">Table of n, a(n) for n = 1..111</a>

%F Empirical for column k:

%F k=1: a(n) = 17*a(n-1) -55*a(n-2) +39*a(n-3)

%F k=2: a(n) = 34*a(n-1) -64*a(n-2)

%F k=3: a(n) = 129*a(n-1) -1759*a(n-2) +7575*a(n-3) -9064*a(n-4) +3120*a(n-5)

%F k=4: a(n) = 373*a(n-1) -4754*a(n-2) +15312*a(n-3)

%F k=5: (order 10)

%F k=6: (order 9)

%F Empirical for row n:

%F n=1: a(k)=6*a(k-1)-7*a(k-2)-6*a(k-3)+8*a(k-4)

%F n=2: a(k)=10*a(k-1)+50*a(k-2)-116*a(k-3)-361*a(k-4)+106*a(k-5)+312*a(k-6)

%F n=3: (order 15)

%F n=4: (order 37)

%e Some solutions for n=4 k=1

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

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

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

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

%Y Column 1 is A198900

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_ Jul 05 2012