A297395 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.

1, 2, 1, 3, 5, 1, 4, 9, 9, 1, 6, 13, 19, 20, 1, 9, 33, 37, 57, 41, 1, 13, 69, 127, 126, 139, 85, 1, 19, 121, 323, 700, 385, 369, 178, 1, 28, 253, 763, 2569, 3175, 1243, 963, 369, 1, 41, 529, 2121, 7779, 14940, 15541, 3924, 2489, 769, 1, 60, 1013, 5557, 31081, 58901, 99682

Offset

1,2

Comments

Table starts

.1...2....3.....4.......6........9........13.........19...........28

.1...5....9....13......33.......69.......121........253..........529

.1...9...19....37.....127......323.......763.......2121.........5557

.1..20...57...126.....700.....2569......7779......31081.......117084

.1..41..139...385....3175....14940.....58901.....325922......1616869

.1..85..369..1243...15541....99682....514945....3977868.....27131403

.1.178..963..3924...74736...640562...4279111...46261441....428200086

.1.369.2489.12477..358341..4101278..35870939..540319235...6780786267

.1.769.6523.39625.1729617.26607999.302197213.6362528482.108762242579

Links

R. H. Hardin, Table of n, a(n) for n = 1..420

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

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

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

k=4: a(n) = a(n-1) +6*a(n-2) +4*a(n-3) -3*a(n-4) -a(n-5) -2*a(n-6) -a(n-7)

k=5: [order 20]

k=6: [order 25]

k=7: [order 55]

Empirical for row n:

n=1: a(n) = a(n-1) +a(n-3)

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

n=3: a(n) = a(n-1) +a(n-2) +8*a(n-3) +a(n-4) -2*a(n-6)

n=4: [order 8]

n=5: [order 21]

n=6: [order 31]

n=7: [order 69]

Example

Some solutions for n=5 k=4
..0..0..1..1. .0..1..1..0. .0..1..0..0. .0..0..1..1. .0..0..0..0
..0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..0..0. .0..0..1..0
..0..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..1
..0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1. .0..1..0..0
..0..0..1..1. .0..0..1..0. .1..1..0..0. .0..0..0..0. .1..0..0..0

Crossrefs

Column 2 is A105309(n+1).

Row 1 is A000930(n+1).

Row 2 is A089977(n+1).

Sequence in context: A047997 A188211 A175009 * A297595 A049069 A030237

Adjacent sequences: A297392 A297393 A297394 * A297396 A297397 A297398

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 29 2017

Status

approved