|
|
A232047
|
|
T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors
|
|
13
|
|
|
2, 2, 4, 4, 7, 8, 7, 15, 21, 16, 12, 34, 80, 65, 32, 21, 79, 318, 446, 200, 64, 37, 184, 1315, 3082, 2477, 616, 128, 65, 426, 5364, 22063, 29974, 13752, 1897, 256, 114, 984, 21680, 153562, 377676, 290672, 76375, 5842, 512, 200, 2274, 87452, 1060850, 4588174
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Table starts
....2.....2........4..........7...........12..............21................37
....4.....7.......15.........34...........79.............184...............426
....8....21.......80........318.........1315............5364.............21680
...16....65......446.......3082........22063..........153562...........1060850
...32...200.....2477......29974.......377676.........4588174..........55505057
...64...616....13752.....290672......6430408.......136134243........2882322121
..128..1897....76375....2821630....109609484......4041385884......149582129861
..256..5842...424115...27382537...1868028342....119990644449.....7766282047395
..512.17991..2355221..265752221..31836538191...3562337669985...403179428472169
.1024.55405.13079032.2579134666.542586883485.105762437152368.20931014633412316
|
|
LINKS
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +3*a(n-2) +a(n-3)
k=3: a(n) = 4*a(n-1) +9*a(n-2) -a(n-3) -6*a(n-4) for n>5
k=4: [order 8] for n>9
k=5: [order 14] for n>15
k=6: [order 24] for n>26
k=7: [order 44] for n>47
Empirical for row n:
n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3) for n>4
n=2: a(n) = 4*a(n-1) -6*a(n-2) +7*a(n-3) -6*a(n-4) +3*a(n-5) -a(n-6) -a(n-7) for n>8
n=3: [order 15] for n>18
n=4: [order 33] for n>36
n=5: [order 78] for n>84
|
|
EXAMPLE
|
Some solutions for n=4 k=4
..0..0..0..1....0..0..0..1....1..0..0..0....0..0..0..0....1..1..0..0
..1..0..1..1....0..0..1..0....0..0..0..0....1..0..0..0....0..0..1..0
..0..0..0..1....0..1..0..0....0..1..0..0....1..1..1..0....0..1..0..1
..1..0..0..0....1..0..0..1....1..0..0..1....1..1..0..0....0..0..1..1
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|