%I #4 Feb 20 2017 07:33:23

%S 2,4,4,7,11,7,13,27,27,13,24,76,99,76,24,44,201,413,413,201,44,81,537,

%T 1601,2638,1601,537,81,149,1444,6349,15460,15460,6349,1444,149,274,

%U 3859,25153,92817,133118,92817,25153,3859,274,504,10339,99287,557439,1190848

%N T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its king-move neighbors.

%C Table starts

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

%C ...4....11......27........76........201..........537...........1444

%C ...7....27......99.......413.......1601.........6349..........25153

%C ..13....76.....413......2638......15460........92817.........557439

%C ..24...201....1601.....15460.....133118......1190848.......10614316

%C ..44...537....6349.....92817....1190848.....15985259......213392087

%C ..81..1444...25153....557439...10614316....213392087.....4257307148

%C .149..3859...99287...3332685...94161619...2835418176....84514081303

%C .274.10339..392907..19979228..838433062..37825158151..1685475197497

%C .504.27692.1553391.119669673.7454215075.503735487244.33544066527869

%H R. H. Hardin, <a href="/A282647/b282647.txt">Table of n, a(n) for n = 1..364</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) +4*a(n-3)

%F k=3: a(n) = 2*a(n-1) +6*a(n-2) +8*a(n-3) -5*a(n-4) +2*a(n-5) -2*a(n-6)

%F k=4: [order 9]

%F k=5: [order 21]

%F k=6: [order 30]

%F k=7: [order 66]

%e Some solutions for n=4 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 20 2017