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A230899
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, no adjacent elements equal, and upper left element zero
7
0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 10, 14, 10, 0, 0, 22, 34, 34, 22, 0, 0, 70, 198, 388, 198, 70, 0, 0, 186, 810, 2722, 2722, 810, 186, 0, 0, 538, 3706, 23884, 40762, 23884, 3706, 538, 0, 0, 1494, 16918, 190364, 579218, 579218, 190364, 16918, 1494, 0, 0, 4230, 76318
OFFSET
1,5
COMMENTS
Table starts
.0...0.....0.......0.........0...........0............0..............0
.0...2.....2......10........22..........70..........186............538
.0...2....14......34.......198.........810.........3706..........16918
.0..10....34.....388......2722.......23884.......190364........1588552
.0..22...198....2722.....40762......579218......8554562......124839450
.0..70...810...23884....579218....15392914....400106488....10548244824
.0.186..3706..190364...8554562...400106488..18831479468...887265863604
.0.538.16918.1588552.124839450.10548244824.887265863604.75228804427354
LINKS
FORMULA
Empirical for column k:
k=2: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3)
k=3: [order 11]
k=4: [order 44] for n>45
EXAMPLE
Some solutions for n=4 k=4
..0..1..0..3....0..1..0..3....0..3..2..3....0..3..2..3....0..3..2..3
..3..2..1..2....3..2..1..2....1..0..1..0....1..2..1..0....1..2..1..0
..2..3..2..3....0..3..0..3....2..3..0..3....2..3..0..1....0..3..2..3
..1..0..1..0....1..2..1..0....1..0..1..2....1..0..3..2....1..2..1..0
CROSSREFS
Sequence in context: A353856 A216800 A230831 * A230805 A230994 A337509
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Oct 31 2013
STATUS
approved