A297224 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 neighboring 1s.

1, 2, 1, 3, 4, 1, 4, 8, 9, 1, 6, 16, 24, 19, 1, 9, 33, 57, 68, 41, 1, 13, 69, 182, 207, 196, 88, 1, 19, 145, 535, 997, 751, 564, 189, 1, 28, 300, 1513, 4210, 5570, 2720, 1620, 406, 1, 41, 624, 4415, 16658, 33158, 30946, 9861, 4660, 872, 1, 60, 1300, 12832, 68769, 178469

Offset

1,2

Comments

Table starts

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

.1...4.....8.....16......33........69........145.........300...........624

.1...9....24.....57.....182.......535.......1513........4415.........12832

.1..19....68....207.....997......4210......16658.......68769........284867

.1..41...196....751....5570.....33158.....178469.....1051514.......6152761

.1..88...564...2720...30946....261939....1918732....16176806.....134671502

.1.189..1620...9861..171851...2063378...20599895...248421807....2936448567

.1.406..4660..35741..955316..16277793..221333623..3819208252...64142817874

.1.872.13396.129540.5308160.128351805.2377449633.58680928294.1400212345305

Links

R. H. Hardin, Table of n, a(n) for n = 1..611

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)

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

k=4: a(n) = a(n-1) +6*a(n-2) +11*a(n-3) +6*a(n-4) +a(n-5)

k=5: [order 9]

k=6: [order 11] for n>13

k=7: [order 16] for n>21

Empirical for row n:

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

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

n=3: [order 13]

n=4: [order 27]

n=5: [order 60]

Example

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

Crossrefs

Column 2 is A078039.

Row 1 is A000930(n+1).

Row 2 is A264166.

Sequence in context: A210211 A283054 A247358 * A180383 A133807 A325001

Adjacent sequences: A297221 A297222 A297223 * A297225 A297226 A297227

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 27 2017

Status

approved