A232076 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every element equal to some horizontal, diagonal or antidiagonal neighbor, with top left element zero.

3, 15, 11, 46, 87, 34, 161, 520, 602, 111, 601, 3681, 6624, 3985, 361, 2208, 26587, 91636, 82996, 26713, 1172, 8053, 189404, 1313477, 2265691, 1043172, 178484, 3809, 29415, 1348429, 18480458, 64298979, 56126173, 13105012, 1193537, 12377, 107534

Offset: 1

Author

R. H. Hardin, Nov 17 2013

Keywords

• nonn
• tabl

Comments

Table starts

......3........15...........46.............161................601

.....11........87..........520............3681..............26587

.....34.......602.........6624...........91636............1313477

....111......3985........82996.........2265691...........64298979

....361.....26713......1043172........56126173.........3154769585

...1172....178484.....13105012......1389867384.......154723539035

...3809...1193537....164650280.....34420057373......7588839921175

..12377...7979619...2068621706....852404560481....372212311236497

..40218..53352090..25989674166..21109624812630..18256039956940439

.130687.356709629.326528021922.522775448585677.895410839428587845

Examples

			Some solutions for n=3 k=4
..0..0..1..1..0....0..0..1..1..1....0..0..0..1..1....0..1..0..0..1
..0..0..0..0..0....1..1..0..0..0....0..0..0..1..0....1..0..0..1..1
..0..0..1..1..1....1..0..0..0..0....0..0..0..0..0....1..1..0..0..1
..1..1..1..1..1....0..0..1..1..1....1..1..1..1..0....1..0..0..1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..199

Crossrefs

Column 1 is A180762(n+1)

Formula

Empirical for column k:

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

k=2: a(n) = 5*a(n-1) +11*a(n-2) +2*a(n-3) -8*a(n-5)

k=3: [order 10]

k=4: [order 30]

k=5: [order 50]

Empirical for row n:

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

n=2: [order 8]

n=3: [order 20]

n=4: [order 54]