A268009 T(n,k)=Number of nXk 0..k arrays with every repeated value in every row and column unequal to the previous repeated value, and new values introduced in row-major sequential order.

1, 2, 2, 4, 14, 3, 12, 159, 96, 5, 40, 3183, 7445, 726, 7, 154, 88243, 1396408, 381958, 5046, 11, 656, 3222467, 454238345, 700411548, 18691624, 35574, 15, 3074, 147078491, 231327070236, 2833253114538, 342829793123, 911680225, 242406, 23

Offset

1,2

Comments

Table starts

..1.......2...........4..............12................40...............154

..2......14.........159............3183.............88243...........3222467

..3......96........7445.........1396408.........454238345......231327070236

..5.....726......381958.......700411548.....2833253114538.21815272076639694

..7....5046....18691624....342829793123.17551555370610669

.11...35574...911680225.166704329683286

.15..242406.43653230106

.23.1653750

.31

Links

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

Formula

Empirical for column k:

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

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

k=3: [order 75]

Example

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

Crossrefs

Column 1 is A052955(n-1).

Column 2 is A267913.

Sequence in context: A130797 A362262 A248238 * A263224 A360922 A267957

Adjacent sequences: A268006 A268007 A268008 * A268010 A268011 A268012

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 24 2016

Status

approved