|
|
A267719
|
|
T(n,k)=Number of nXk 0..1 arrays with every repeated value in every row and column greater than the previous repeated value.
|
|
7
|
|
|
2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 12, 81, 102, 81, 12, 16, 144, 270, 270, 144, 16, 20, 256, 546, 872, 546, 256, 20, 25, 400, 1080, 1915, 1915, 1080, 400, 25, 30, 625, 1866, 4266, 4444, 4266, 1866, 625, 30, 36, 900, 3186, 7879, 10489, 10489, 7879, 3186, 900, 36, 42, 1296
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Table starts
..2....4....6.....9.....12.....16.....20......25......30.......36.......42
..4...16...36....81....144....256....400.....625.....900.....1296.....1764
..6...36..102...270....546...1080...1866....3186....5010.....7830....11550
..9...81..270...872...1915...4266...7879...14632...24440....40816....63714
.12..144..546..1915...4444..10489..20226...39485...68430...119560...192852
.16..256.1080..4266..10489..26906..54887..114392..209470...385962...656670
.20..400.1866..7879..20226..54887.116036..255009..481390...932245..1627470
.25..625.3186.14632..39485.114392.255009..592110.1179367..2391952..4403235
.30..900.5010.24440..68430.209470.481390.1179367.2411426..5148115..9689432
.36.1296.7830.40816.119560.385962.932245.2391952.5148115.11438402.22656990
|
|
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
k=7: [order 28] for n>30
|
|
EXAMPLE
|
Some solutions for n=5 k=4
..1..0..0..1....0..1..1..0....1..1..0..1....0..1..1..0....1..0..0..1
..1..0..1..1....1..0..0..1....0..1..1..0....1..0..0..1....1..0..1..1
..0..1..0..0....0..1..1..0....1..0..1..1....0..0..1..0....0..1..0..0
..1..1..0..1....1..0..1..1....0..1..0..0....0..1..0..0....1..0..1..1
..0..0..1..0....1..1..0..1....1..0..1..0....1..1..0..1....0..1..0..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|