A297020 - OEIS

%I #4 Dec 23 2017 15:06:06

%S 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,

%T 135,150,150,135,31,1,1,71,400,590,852,590,400,71,1,1,166,1310,2355,

%U 5878,5878,2355,1310,166,1,1,365,4481,9521,36508,74534,36508,9521,4481,365,1

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

%C Table starts

%C .1...1....1.....1.......1.........1..........1............1.............1

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

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

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

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

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

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

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

%C .1.166.4481.39410.1897582.108002628.3611228309.164053152053.8482089381228

%H R. H. Hardin, <a href="/A297020/b297020.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

%F 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)

%F k=3: [order 20]

%F k=4: [order 48]

%e Some solutions for n=6 k=4

%e ..0..0..1..1. .0..1..1..0. .1..1..0..0. .0..0..1..1. .0..0..1..1

%e ..0..0..1..1. .0..1..1..1. .1..1..1..0. .0..1..1..1. .0..1..1..1

%e ..0..0..0..0. .0..0..1..1. .1..0..1..0. .1..0..0..0. .1..1..0..1

%e ..0..1..1..0. .0..0..0..0. .1..0..1..1. .1..1..1..0. .1..1..1..1

%e ..1..1..1..1. .1..1..0..0. .1..1..1..0. .1..1..1..1. .1..0..1..1

%e ..0..1..1..0. .1..1..0..0. .1..1..0..0. .0..0..1..1. .0..1..1..0

%Y Column 2 is A296109.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Dec 23 2017