login
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
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 20 2016
STATUS
approved