A268092 T(n,k)=Number of nXk 0..2 arrays with every repeated value in every row not one larger and in every column one larger mod 3 than the previous repeated value, and upper left element zero.

1, 3, 3, 9, 27, 8, 26, 243, 192, 21, 74, 2028, 4608, 1323, 53, 208, 16428, 98830, 83349, 8427, 132, 580, 129792, 2028304, 4523326, 1339893, 52272, 323, 1608, 1009200, 40109966, 231625525, 176935858, 20699712, 312987, 783, 4440, 7756992, 774613334

Offset

1,2

Comments

Table starts

....1........3............9..............26................74...............208

....3.......27..........243............2028.............16428............129792

....8......192.........4608...........98830...........2028304..........40109966

...21.....1323........83349.........4523326.........231625525.......11291781118

...53.....8427......1339893.......176935858.......21743763815.....2513690254246

..132....52272.....20699712......6564461764.....1911026997488...517166705601727

..323...312987....303284403....226972598646...153835391484442.95786441193596382

..783..1839267...4320438183...7559736791208.11819612140199748

.1880.10603200..59802048000.242339515066412

.4485.60345675.811951057125

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for column k:

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

k=2: a(n) = 10*a(n-1) -8*a(n-2) -163*a(n-3) +306*a(n-4) +684*a(n-5) -1296*a(n-6)

k=3: [order 10]

Empirical for row n:

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

n=2: a(n) = 14*a(n-1) -44*a(n-2) -88*a(n-3) +352*a(n-4) +320*a(n-5) -256*a(n-6)

Example

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

Crossrefs

Column 1 is A267946.

Column 2 is A267947.

Sequence in context: A215885 A176158 A083008 * A229024 A117976 A010098

Adjacent sequences: A268089 A268090 A268091 * A268093 A268094 A268095

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 26 2016

Status

approved