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A230805
T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, and upper left element zero
6
0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 16, 14, 16, 0, 0, 34, 40, 40, 34, 0, 0, 154, 298, 1370, 298, 154, 0, 0, 432, 1546, 10448, 10448, 1546, 432, 0, 0, 1618, 8704, 183088, 243746, 183088, 8704, 1618, 0, 0, 5058, 50450, 2045378, 6832578, 6832578, 2045378, 50450, 5058, 0, 0
OFFSET
1,5
COMMENTS
Table starts
.0....0.....0........0..........0.............0.............0.............0
.0....2.....2.......16.........34...........154...........432..........1618
.0....2....14.......40........298..........1546..........8704.........50450
.0...16....40.....1370......10448........183088.......2045378......29175688
.0...34...298....10448.....243746.......6832578.....180981600....4943014834
.0..154..1546...183088....6832578.....485186602...25669880656.1576356652138
.0..432..8704..2045378..180981600...25669880656.3006220926554
.0.1618.50450.29175688.4943014834.1576356652138
LINKS
FORMULA
Empirical for column k:
k=2: a(n) = 2*a(n-1) +6*a(n-2) -5*a(n-3)
k=3: [order 13]
k=4: [order 68]
EXAMPLE
Some solutions for n=4 k=4
..0..1..3..0....0..1..1..2....0..3..2..1....0..1..3..0....0..3..2..3
..3..2..2..1....3..2..0..3....1..2..3..0....3..2..2..1....1..2..1..0
..1..0..1..2....3..2..0..3....3..0..0..1....0..1..2..3....0..3..0..3
..2..3..0..3....0..1..1..2....2..1..3..2....3..2..1..0....3..2..1..2
CROSSREFS
Sequence in context: A216800 A230831 A230899 * A230994 A337509 A144734
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Oct 30 2013
STATUS
approved