A232047 T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors

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

R. H. Hardin, Table of n, a(n) for n = 1..478

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

Adjacent sequences: A232044 A232045 A232046 * A232048 A232049 A232050

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 17 2013

Status

approved