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

Author

R. H. Hardin, Jan 20 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A002620(n+2).

Column 2 is A030179(n+2).

Row 1 is A029907(n+1).

Row 2 is A267729.

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]