A267911 T(n,k)=Number of nXk 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

1, 2, 2, 4, 14, 5, 11, 96, 122, 13, 29, 726, 2304, 938, 34, 77, 5046, 47916, 43972, 6734, 88, 201, 35574, 878004, 2331981, 754852, 45938, 225, 525, 242406, 16435188, 104491831, 98614986, 12017350, 302402, 569, 1361, 1653750, 292341636

Offset

1,2

Comments

Table starts

....1........2............4..............11...............29................77

....2.......14...........96.............726.............5046.............35574

....5......122.........2304...........47916...........878004..........16435188

...13......938........43972.........2331981........104491831........4817531571

...34.....6734.......754852........98614986......10441322974.....1145682971200

...88....45938.....12017350......3774659262.....922017784240...235078226435316

..225...302402....181535822....134786758099...74691010105571.43513012231778789

..569..1939154...2638824216...4574297266940.5680483902454184

.1426.12192302..37263580006.149403639631334

.3548.75508538.514648921140

Links

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

Formula

Empirical for column k:

k=1: a(n) = 5*a(n-1) -7*a(n-2) +a(n-3) +2*a(n-4)

k=2: a(n) = 14*a(n-1) -60*a(n-2) +50*a(n-3) +145*a(n-4) -80*a(n-5) -84*a(n-6) +16*a(n-7)

k=3: [order 54]

Empirical for row n:

n=1: a(n) = 3*a(n-1) +2*a(n-2) -8*a(n-3) for n>5

n=2: [order 6] for n>8

n=3: [order 10] for n>12

Example

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

Crossrefs

Sequence in context: A204705 A206650 A268049 * A120654 A121514 A121526

Adjacent sequences: A267908 A267909 A267910 * A267912 A267913 A267914

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 22 2016

Status

approved