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

1,1

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A180762(n+1)

Sequence in context: A337471 A145179 A297897 * A329770 A099476 A063628

Adjacent sequences: A232073 A232074 A232075 * A232077 A232078 A232079

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 17 2013

Status

approved