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A297299
T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 2 neighboring 1s.
10
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 27 2017
STATUS
approved