%I #8 Jun 19 2020 04:02:33
%S 2,3,3,5,10,5,8,25,25,8,13,68,82,68,13,21,208,334,334,208,21,34,609,
%T 1451,2295,1451,609,34,55,1785,5938,16541,16541,5938,1785,55,89,5375,
%U 25144,110036,213800,110036,25144,5375,89,144,16174,108174,775010,2358963
%N T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 2 or 3 king-move neighboring 1s.
%H R. H. Hardin, <a href="/A296674/b296674.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 3*a(n-1) +5*a(n-3) -10*a(n-4) -12*a(n-5) -4*a(n-6)
%F k=3: [order 12]
%F k=4: [order 27]
%F k=5: [order 67]
%e Table starts
%e ..2.....3......5........8.........13...........21.............34
%e ..3....10.....25.......68........208..........609...........1785
%e ..5....25.....82......334.......1451.........5938..........25144
%e ..8....68....334.....2295......16541.......110036.........775010
%e .13...208...1451....16541.....213800......2358963.......28341757
%e .21...609...5938...110036....2358963.....40937523......794602323
%e .34..1785..25144...775010...28341757....794602323....25499216805
%e .55..5375.108174..5466936..346828018..15702927104...833656369935
%e .89.16174.463106.38297415.4150012532.301022037125.26222808591554
%e ...
%e Some solutions for n=4 k=4
%e ..1..1..1..0. .0..0..0..0. .0..1..1..0. .0..1..0..0. .0..0..1..1
%e ..1..0..0..1. .1..0..0..0. .0..0..1..0. .0..0..0..0. .0..0..0..1
%e ..1..0..1..0. .0..0..0..0. .0..0..0..0. .1..0..0..1. .1..1..1..0
%e ..1..1..0..0. .1..0..0..1. .1..0..0..1. .1..1..0..0. .1..0..0..0
%Y Column 1 is A000045(n+2).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 18 2017