A297299 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 2 neighboring 1s.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 4, 5, 5, 1, 1, 1, 6, 9, 10, 8, 1, 1, 1, 9, 17, 21, 19, 13, 1, 1, 1, 13, 32, 50, 49, 36, 21, 1, 1, 1, 19, 60, 130, 157, 114, 69, 34, 1, 1, 1, 28, 113, 332, 600, 495, 266, 131, 55, 1, 1, 1, 41, 213, 840, 2161, 2816, 1574, 620, 250, 89, 1, 1, 1

Offset

1,8

Comments

Table starts

.1.1..1...1....1.....1......1.......1........1.........1..........1...........1

.1.1..2...3....4.....6......9......13.......19........28.........41..........60

.1.1..3...5....9....17.....32......60......113.......213........401.........755

.1.1..5..10...21....50....130.....332......840......2128.......5408.......13772

.1.1..8..19...49...157....600....2161.....7479.....25639......88307......306281

.1.1.13..36..114...495...2816...14138....64406....288079....1310914.....6040052

.1.1.21..69..266..1574..13504...93906...551477...3159693...18792129...113862870

.1.1.34.131..620..5031..65521..629563..4738693..34652662..269300602..2142898994

.1.1.55.250.1446.16123.319835.4235806.40753529.379882818.3857849537.40317718384

Links

R. H. Hardin, Table of n, a(n) for n = 1..680

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1)

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

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

k=5: a(n) = 2*a(n-1) +2*a(n-2) -2*a(n-3) -2*a(n-4) for n>5

k=6: a(n) = 4*a(n-1) -8*a(n-3) -2*a(n-4) +4*a(n-5) +4*a(n-6) +a(n-7) -a(n-8)

k=7: [order 12] for n>14

Empirical for row n:

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

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

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

n=4: [order 13] for n>16

n=5: [order 32] for n>37

n=6: [order 68] for n>76

Example

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

Crossrefs

Column 3 is A000045(n+1).

Column 4 is A158943(n+1).

Row 2 is A000930.

Sequence in context: A193516 A124445 A124279 * A135225 A208891 A177767

Adjacent sequences: A297296 A297297 A297298 * A297300 A297301 A297302

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 27 2017

Status

approved