A283634 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly two elements.

0, 0, 0, 0, 0, 0, 1, 0, 6, 0, 2, 36, 37, 28, 0, 5, 88, 639, 388, 142, 0, 13, 516, 2875, 7742, 3729, 606, 0, 29, 2076, 21963, 61592, 85469, 28828, 2458, 0, 65, 7372, 127635, 700534, 1185010, 856710, 203025, 9520, 0, 143, 27108, 693783, 6345928, 19517898, 20051838

Offset

1,9

Comments

Table starts

.0......0........0..........1............2...............5................13

.0......0........0.........36...........88.............516..............2076

.0......6.......37........639.........2875...........21963............127635

.0.....28......388.......7742........61592..........700534...........6345928

.0....142.....3729......85469......1185010........19517898.........272974255

.0....606....28828.....856710.....20051838.......490925804.......10666178322

.0...2458...203025....8209582....317384829.....11651389723......392539665568

.0...9520..1325980...75625580...4754748994....264077146748....13797245749346

.0..35678..8216341..677582140..68462751532...5787991095939...468742166961530

.0.130398.48912768.5935472812.955500406758.123521985310158.15502521715119538

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

k=2: [order 12]

k=3: [order 18]

k=4: [order 24]

k=5: [order 63]

k=6: [order 81]

Empirical for row n:

n=1: a(n) = 3*a(n-1) -2*a(n-3) -6*a(n-4) +4*a(n-6) +6*a(n-7) +3*a(n-8) +a(n-9)

n=2: [order 9]

n=3: [order 18]

n=4: [order 24] for n>26

n=5: [order 63]

n=6: [order 96]

Example

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

Crossrefs

Column 2 is A283094.

Row 1 is A282831.

Sequence in context: A366349 A075092 A152244 * A179641 A110993 A262697

Adjacent sequences: A283631 A283632 A283633 * A283635 A283636 A283637

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 12 2017

Status

approved