A231080 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, 2, 0, 0, 14, 2, 0, 0, 40, 50, 16, 0, 0, 356, 136, 784, 34, 0, 0, 1840, 2820, 6400, 5098, 154, 0, 0, 10128, 38000, 523936, 71944, 54426, 432, 0, 0, 60808, 421920, 18937480, 18655220, 1866192, 441392, 1618, 0, 0, 337016, 6118120, 696453136

Offset

1,5

Comments

Table starts

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

.0....2......14........40...........356...........1840...........10128

.0....2......50.......136..........2820..........38000..........421920

.0...16.....784......6400........523936.......18937480.......696453136

.0...34....5098.....71944......18655220.....1782634608....190102522528

.0..154...54426...1866192....1480839364...417868659864.131563996224512

.0..432..441392..32292680...79624748768.61990953794520

.0.1618.4164402.679262904.5187293040908

Links

R. H. Hardin, Table of n, a(n) for n = 1..83

Formula

Empirical for column k:

k=2: a(n) = 2*a(n-1) +6*a(n-2) -5*a(n-3)

k=3: [order 11]

k=4: [order 36]

Empirical for row n:

n=2: a(n) = 3*a(n-1) +12*a(n-2) +30*a(n-3) -64*a(n-4) +16*a(n-5)

n=3: [order 35]

Example

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

Crossrefs

Column 2 is A230800

Sequence in context: A061848 A193294 A231049 * A231246 A216991 A191418

Adjacent sequences: A231077 A231078 A231079 * A231081 A231082 A231083

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 03 2013

Status

approved