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

Author

R. H. Hardin, Dec 27 2017

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 2 is A078039.

Row 1 is A000930(n+1).

Row 2 is A264166.

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]