A230926 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally, vertically, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3 and at least one element with value (x(i,j)-1) mod 3, and upper left element zero

0, 0, 0, 0, 12, 0, 0, 54, 54, 0, 0, 432, 408, 432, 0, 0, 3108, 8748, 8748, 3108, 0, 0, 22428, 154632, 559872, 154632, 22428, 0, 0, 162504, 2772906, 28978992, 28978992, 2772906, 162504, 0, 0, 1175592, 49910578, 1509045552, 4265306528, 1509045552, 49910578

Offset

1,5

Comments

Table starts

.0.......0.........0.............0.................0....................0

.0......12........54...........432..............3108................22428

.0......54.......408..........8748............154632..............2772906

.0.....432......8748........559872..........28978992...........1509045552

.0....3108....154632......28978992........4265306528.........635678359988

.0...22428...2772906....1509045552......635678359988......270258566366420

.0..162504..49910578...79222650048....95355343910570...115824906242444524

.0.1175592.896666568.4146049651392.14264086558627070.49485565220035538028

Links

R. H. Hardin, Table of n, a(n) for n = 1..127

Formula

Empirical for column k:

k=2: a(n) = 5*a(n-1) +14*a(n-2) +16*a(n-3) -2*a(n-4) +4*a(n-5)

k=3: [order 17]

k=4: [order 15]

Example

Some solutions for n=3 k=4
..0..2..1..0....0..1..0..2....0..0..1..0....0..0..0..2....0..1..2..2
..1..2..1..2....2..1..1..2....1..2..2..0....1..2..1..2....2..2..1..0
..1..0..2..0....0..0..2..0....0..1..1..1....0..0..0..1....1..0..2..2

Crossrefs

Sequence in context: A023917 A359001 A347802 * A064141 A230526 A156401

Adjacent sequences: A230923 A230924 A230925 * A230927 A230928 A230929

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 01 2013

Status

approved