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

Author

R. H. Hardin, Nov 16 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A207170 for n>1

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]