A268003 T(n,k)=Number of nXk 0..k arrays with every repeated value in every row and column equal to the previous repeated value, and new values introduced in row-major sequential order.

1, 2, 2, 5, 14, 4, 14, 187, 122, 7, 45, 3552, 11051, 938, 12, 163, 93311, 1880990, 605969, 6734, 20, 657, 3201247, 555258347, 982227549, 30785259, 45938, 33, 2910, 137687080, 256785961187, 3511764501993, 477324637497, 1470330667, 302402, 54

Offset: 1

Author

R. H. Hardin, Jan 24 2016

Keywords

• nonn
• tabl

Comments

Table starts

..1.......2...........5..............14................45...............163

..2......14.........187............3552.............93311...........3201247

..4.....122.......11051.........1880990.........555258347......256785961187

..7.....938......605969.......982227549.....3511764501993.23932385578547037

.12....6734....30785259....477324637497.20888913167378133

.20...45938..1470330667.217487430054270

.33..302402.67008101445

.54.1939154

.88

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..45

Crossrefs

Column 1 is A000071(n+2).

Column 2 is A267906.

Formula

Empirical for column k:

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

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 20]