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A283691
T(n,k) = Number of n X k 0..1 arrays with no 1 equal to more than two of its horizontal, diagonal and antidiagonal neighbors.
13
2, 4, 4, 8, 16, 8, 16, 49, 57, 16, 32, 161, 264, 209, 32, 64, 548, 1521, 1525, 768, 64, 128, 1824, 8687, 15226, 8732, 2816, 128, 256, 6081, 47829, 149840, 150497, 49924, 10329, 256, 512, 20353, 268285, 1392868, 2530461, 1489917, 285770, 37889, 512, 1024
OFFSET
1,1
COMMENTS
Table starts
...2......4.......8.........16...........32.............64..............128
...4.....16......49........161..........548...........1824.............6081
...8.....57.....264.......1521.........8687..........47829...........268285
..16....209....1525......15226.......149840........1392868.........13354587
..32....768....8732.....150497......2530461.......39372084........640543058
..64...2816...49924....1489917.....42865601.....1119189256......30968693109
.128..10329..285770...14754038....726353972....31815868749....1496646288297
.256..37889.1635402..146079023..12304063774...904083654190...72299799564414
.512.138980.9359104.1446386879.208447516852.25694926726796.3493423029563345
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1).
k=2: a(n) = 3*a(n-1) +2*a(n-2) +2*a(n-3) -a(n-4) -a(n-5).
k=3: [order 10].
k=4: [order 14].
k=5: [order 40].
k=6: [order 83].
Empirical for row n:
n=1: a(n) = 2*a(n-1).
n=2: a(n) = 3*a(n-1) +a(n-2) +3*a(n-3) -6*a(n-4) -8*a(n-5).
n=3: [order 11].
n=4: [order 23].
n=5: [order 56].
EXAMPLE
Some solutions for n=4, k=4
..1..0..1..1. .1..0..0..0. .0..0..1..0. .0..0..0..1. .1..0..1..0
..0..0..0..0. .1..0..1..0. .0..0..0..1. .0..0..0..0. .1..0..0..0
..1..1..0..1. .0..1..0..0. .0..0..0..1. .0..1..1..0. .0..0..0..1
..1..0..0..1. .0..1..0..1. .1..0..0..1. .1..0..0..0. .0..0..0..1
CROSSREFS
Column 1 is A000079.
Column 2 is A283124.
Row 1 is A000079.
Sequence in context: A189779 A262338 A368043 * A283130 A295716 A282399
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 14 2017
STATUS
approved