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A297224
T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 neighboring 1s.
12
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
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 A374896 A133807
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 27 2017
STATUS
approved