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

Author

R. H. Hardin, Jan 22 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

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