A296651 - OEIS

%I #4 Dec 17 2017 15:48:49

%S 2,4,4,7,12,7,13,29,29,13,24,85,111,85,24,44,248,468,468,248,44,81,

%T 664,1985,3159,1985,664,81,149,1897,8126,20782,20782,8126,1897,149,

%U 274,5385,33933,130303,212537,130303,33933,5385,274,504,14924,141664,849983

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

%C Table starts

%C ...2.....4......7.......13.........24...........44............81

%C ...4....12.....29.......85........248..........664..........1897

%C ...7....29....111......468.......1985.........8126.........33933

%C ..13....85....468.....3159......20782.......130303........849983

%C ..24...248...1985....20782.....212537......2022756......20337282

%C ..44...664...8126...130303....2022756.....29547816.....453231742

%C ..81..1897..33933...849983...20337282....453231742...10730354337

%C .149..5385.141664..5499124..202790850...6893592668..250993766141

%C .274.14924.588156.35347256.1998068553.103949473092.5814109226770

%H R. H. Hardin, <a href="/A296651/b296651.txt">Table of n, a(n) for n = 1..241</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2) +a(n-3)

%F k=2: a(n) = a(n-1) +3*a(n-2) +9*a(n-3) -4*a(n-4) -12*a(n-5) -4*a(n-6)

%F k=3: [order 10]

%F k=4: [order 22]

%F k=5: [order 58]

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A000073(n+3).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 17 2017