|
|
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.
|
|
12
|
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|