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A283691 T(n,k)=Number of nXk 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 (list; table; graph; refs; listen; history; text; internal format)
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

R. H. Hardin, Table of n, a(n) for n = 1..264

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: A189343 A189779 A262338 * A283130 A295716 A282399

Adjacent sequences:  A283688 A283689 A283690 * A283692 A283693 A283694

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 14 2017

STATUS

approved

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Last modified January 23 12:51 EST 2022. Contains 350511 sequences. (Running on oeis4.)