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

1,2

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000071(n+2).

Column 2 is A267906.

Sequence in context: A032290 A032201 A268180 * A208434 A336110 A275352

Adjacent sequences: A268000 A268001 A268002 * A268004 A268005 A268006

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 24 2016

Status

approved