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A214141
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
1, 1, 4, 4, 17, 33, 11, 257, 514, 380, 40, 3074, 28278, 16388, 4801, 147, 40434, 1101051, 3221873, 524296, 62004, 568, 522515, 47730973, 396246659, 367793014, 16777232, 804833, 2227, 6800539, 2000093424, 56449101747, 142612676441, 41989913081
OFFSET
1,3
COMMENTS
Table starts
....1......1.........4...........11.............40...............147
....4.....17.......257.........3074..........40434............522515
...33....514.....28278......1101051.......47730973........2000093424
..380..16388...3221873....396246659....56449101747.....7658621867351
.4801.524296.367793014.142612676441.66761857485037.29325981412599886
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 17*a(n-1) -55*a(n-2) +39*a(n-3)
k=2: a(n) = 34*a(n-1) -64*a(n-2)
k=3: a(n) = 129*a(n-1) -1759*a(n-2) +7575*a(n-3) -9064*a(n-4) +3120*a(n-5)
k=4: a(n) = 373*a(n-1) -4754*a(n-2) +15312*a(n-3)
k=5: (order 10)
k=6: (order 9)
Empirical for row n:
n=1: a(k)=6*a(k-1)-7*a(k-2)-6*a(k-3)+8*a(k-4)
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)
n=3: (order 15)
n=4: (order 37)
EXAMPLE
Some solutions for n=4 k=1
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..2..3....1..2....1..2....1..0....2..3....1..0....2..3....1..0....2..3....2..0
..3..2....2..0....2..3....2..1....0..4....2..3....3..2....2..3....1..4....0..1
..4..0....3..4....1..0....1..2....1..0....0..4....2..0....3..4....4..3....1..3
CROSSREFS
Column 1 is A198900
Sequence in context: A117785 A117787 A113727 * A193961 A368197 A205110
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Jul 05 2012
STATUS
approved