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A297020
T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 3, 4 or 6 king-move neighboring 1s.
7
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 23 2017
STATUS
approved