%I #4 Nov 29 2017 18:17:33

%S 2,3,3,5,6,5,8,13,13,8,13,28,39,28,13,21,60,115,115,60,21,34,129,337,

%T 467,337,129,34,55,277,993,1880,1880,993,277,55,89,595,2919,7604,

%U 10290,7604,2919,595,89,144,1278,8587,30721,56955,56955,30721,8587,1278,144,233

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

%C Table starts

%C ..2....3.....5......8......13........21.........34..........55............89

%C ..3....6....13.....28......60.......129........277.........595..........1278

%C ..5...13....39....115.....337.......993.......2919........8587.........25257

%C ..8...28...115....467....1880......7604......30721......124117........501512

%C .13...60...337...1880...10290.....56955.....314044.....1732883.......9562608

%C .21..129...993...7604...56955....431844....3261576....24650278.....186318117

%C .34..277..2919..30721..314044...3261576...33703065...348555744....3605337986

%C .55..595..8587.124117.1732883..24650278..348555744..4933593439...69844332764

%C .89.1278.25257.501512.9562608.186318117.3605337986.69844332764.1353357158724

%H R. H. Hardin, <a href="/A295918/b295918.txt">Table of n, a(n) for n = 1..311</a>

%F Empirical for column k:

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

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

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

%F k=4: a(n) = 2*a(n-1) +7*a(n-2) +6*a(n-3) -3*a(n-4) -4*a(n-5) +a(n-6)

%F k=5: [order 38]

%F k=6: [order 92]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000045(n+2).

%Y Column 2 is A002478(n+1).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 29 2017