A231037 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally, 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, 0, 0, 0, 0, 2, 0, 0, 4, 10, 0, 0, 0, 0, 72, 32, 2, 0, 0, 32, 736, 1344, 278, 12, 0, 0, 80, 9726, 17984, 20250, 2988, 18, 0, 0, 560, 96882, 677204, 783848, 375620, 23058, 56, 0, 0, 2080, 1194032, 18856728, 79772488, 36327118, 6620496, 199272, 170, 0, 0

Offset

1,9

Comments

Table starts

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

.0..0......0.........4...........0..............32..............80

.0..2.....10........72.........736............9726...........96882

.0..0.....32......1344.......17984..........677204........18856728

.0..2....278.....20250......783848........79772488......5472540636

.0.12...2988....375620....36327118.....10140483166...1844073908022

.0.18..23058...6620496..1587011224...1171740348034.555813932009140

.0.56.199272.114765278.69795938150.139409083454936

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

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

k=3: [order 9]

k=4: [order 37]

Empirical for row n:

n=2: a(n) = 3*a(n-1) +6*a(n-2) +32*a(n-4) -20*a(n-5) +24*a(n-6) -16*a(n-7)

n=3: [order 33] for n>34

Example

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

Crossrefs

Column 2 is A230813

Sequence in context: A153772 A197007 A011449 * A048243 A159814 A169774

Adjacent sequences: A231034 A231035 A231036 * A231038 A231039 A231040

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 03 2013

Status

approved