A231977 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element having a strict majority of its horizontal and vertical neighbors equal to one

9, 16, 16, 36, 56, 36, 81, 169, 169, 81, 169, 550, 841, 550, 169, 361, 1764, 4489, 4489, 1764, 361, 784, 5680, 24964, 43983, 24964, 5680, 784, 1681, 18225, 136900, 417316, 417316, 136900, 18225, 1681, 3600, 58596, 741321, 3844551, 6507601, 3844551

Offset

1,1

Comments

Table starts

....9.....16........36..........81...........169..............361

...16.....56.......169.........550..........1764.............5680

...36....169.......841........4489.........24964...........136900

...81....550......4489.......43983........417316..........3844551

..169...1764.....24964......417316.......6507601........100540729

..361...5680....136900.....3844551.....100540729.......2641967397

..784..18225....741321....35366809....1557328369......69043343121

.1681..58596...4024036...328433132...24225988609....1809552010404

.3600.188356..21911761..3052452001..376708702756...47496507516441

.7744.605458.119268241.28290095075.5849616285604.1245162776547248

Links

R. H. Hardin, Table of n, a(n) for n = 1..475

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6)

k=2: a(n) = 3*a(n-1) +2*a(n-3) +4*a(n-4) -10*a(n-5) -2*a(n-6) -a(n-8) +a(n-9)

k=3: [order 21]

k=4: [order 49]

Example

Some solutions for n=2 k=4
..0..1..1..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..1..0
..0..0..0..0..0....1..0..0..0..0....0..1..0..0..0....0..0..0..0..0
..1..0..0..1..0....0..0..0..1..0....0..1..0..0..0....1..0..0..1..1

Crossrefs

Column 1 is A207170 for n>1

Sequence in context: A092095 A186851 A201266 * A269563 A217570 A274188

Adjacent sequences: A231974 A231975 A231976 * A231978 A231979 A231980

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 16 2013

Status

approved