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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
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
Column 1 is A000079
Column 2 is A218836
Row 1 is A005251(n+2)
Sequence in context: A368688 A208963 A011142 * A060029 A100471 A266777
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 17 2013
STATUS
approved