A297085 - OEIS

%I #4 Dec 25 2017 08:40:52

%S 2,4,4,7,12,7,13,30,30,13,24,96,136,96,24,44,286,687,687,286,44,81,

%T 848,3616,6784,3616,848,81,149,2620,19277,64819,64819,19277,2620,149,

%U 274,7964,105494,654120,1180260,654120,105494,7964,274,504,24332,581688

%N T(n,k)=Number of nXk 0..1 arrays with no 1 adjacent to 2 king-move neighboring 1s.

%C Table starts

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

%C ...4....12......30........96..........286............848..............2620

%C ...7....30.....136.......687.........3616..........19277............105494

%C ..13....96.....687......6784........64819.........654120...........6743851

%C ..24...286....3616.....64819......1180260.......22630723.........444282892

%C ..44...848...19277....654120.....22630723......833228038.......31284950414

%C ..81..2620..105494...6743851....444282892....31284950414.....2245841563645

%C .149..7964..581688..69857453...8764056739..1180379285603...161959380452328

%C .274.24332.3225186.727765313.173651084724.44714930487805.11725115199949679

%H R. H. Hardin, <a href="/A297085/b297085.txt">Table of n, a(n) for n = 1..220</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) = 2*a(n-1) +4*a(n-2) +4*a(n-3) -14*a(n-4) -14*a(n-5) -4*a(n-6)

%F k=3: [order 17]

%F k=4: [order 34]

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 25 2017