A267788 T(n,k)=Number of nXk 0..1 arrays with every repeated value in every row greater than or equal to, and in every column greater than, the previous repeated value.

2, 4, 4, 8, 16, 6, 15, 64, 36, 9, 28, 225, 216, 81, 12, 51, 784, 1056, 729, 144, 16, 92, 2601, 5004, 5081, 1728, 256, 20, 164, 8464, 22110, 34173, 14956, 4096, 400, 25, 290, 26896, 94554, 211555, 122770, 44742, 8000, 625, 30, 509, 84100, 391314, 1262760, 912667

Offset

1,1

Comments

Table starts

..2....4.....8.....15.......28........51.........92.........164..........290

..4...16....64....225......784......2601.......8464.......26896........84100

..6...36...216...1056.....5004.....22110......94554......391314......1582824

..9...81...729...5081....34173....211555....1262760.....7263481.....40755550

.12..144..1728..14956...122770....912667....6484282....44116906....291598056

.16..256..4096..44742...460598...4245574...37282358...312449872...2540944329

.20..400..8000.102954..1234716..13126812..132388406..1271314080..11831791048

.25..625.15625.238813..3380133..42012357..494152778..5520112546..59723941668

.30..900.27000.472174..7591852.106570618.1413416776.17806098826.217360101006

.36.1296.46656.935890.17155354.272337497.4075463059.57801662876.793861159136

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +2*a(n-2) -6*a(n-3) +6*a(n-5) -2*a(n-6) -2*a(n-7) +a(n-8)

k=3: [order 12]

k=4: [order 16] for n>18

k=5: [order 20] for n>22

k=6: [order 24] for n>27

Empirical for row n:

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

n=2: [order 9]

n=3: [order 12]

n=4: [order 93]

Example

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

Crossrefs

Column 1 is A002620(n+2).

Column 2 is A030179(n+2).

Row 1 is A029907(n+1).

Row 2 is A267729.

Sequence in context: A297094 A283282 A181253 * A189696 A189196 A188747

Adjacent sequences: A267785 A267786 A267787 * A267789 A267790 A267791

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 20 2016

Status

approved