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

Author

R. H. Hardin, Nov 17 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079

Column 2 is A218836

Row 1 is A005251(n+2)

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