A297020 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 3, 4 or 6 king-move neighboring 1s.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 8, 4, 1, 1, 8, 14, 14, 8, 1, 1, 17, 39, 46, 39, 17, 1, 1, 31, 135, 150, 150, 135, 31, 1, 1, 71, 400, 590, 852, 590, 400, 71, 1, 1, 166, 1310, 2355, 5878, 5878, 2355, 1310, 166, 1, 1, 365, 4481, 9521, 36508, 74534, 36508, 9521, 4481, 365, 1

Offset

1,5

Comments

Table starts

.1...1....1.....1.......1.........1..........1............1.............1

.1...2....3.....4.......8........17.........31...........71...........166

.1...3....8....14......39.......135........400.........1310..........4481

.1...4...14....46.....150.......590.......2355.........9521.........39410

.1...8...39...150.....852......5878......36508.......257339.......1897582

.1..17..135...590....5878.....74534.....732736......8605648.....108002628

.1..31..400..2355...36508....732736...11172600....193972861....3611228309

.1..71.1310..9521..257339...8605648..193972861...5380073625..164053152053

.1.166.4481.39410.1897582.108002628.3611228309.164053152053.8482089381228

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +2*a(n-2) +5*a(n-3) -2*a(n-4) -6*a(n-5) -4*a(n-6)

k=3: [order 20]

k=4: [order 48]

Example

Some solutions for n=6 k=4
..0..0..1..1. .0..1..1..0. .1..1..0..0. .0..0..1..1. .0..0..1..1
..0..0..1..1. .0..1..1..1. .1..1..1..0. .0..1..1..1. .0..1..1..1
..0..0..0..0. .0..0..1..1. .1..0..1..0. .1..0..0..0. .1..1..0..1
..0..1..1..0. .0..0..0..0. .1..0..1..1. .1..1..1..0. .1..1..1..1
..1..1..1..1. .1..1..0..0. .1..1..1..0. .1..1..1..1. .1..0..1..1
..0..1..1..0. .1..1..0..0. .1..1..0..0. .0..0..1..1. .0..1..1..0

Crossrefs

Column 2 is A296109.

Sequence in context: A202756 A156354 A295205 * A099597 A358146 A283113

Adjacent sequences: A297017 A297018 A297019 * A297021 A297022 A297023

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 23 2017

Status

approved