%I #4 Dec 17 2017 15:12:48
%S 1,2,2,4,10,4,7,28,28,7,12,86,132,86,12,21,279,671,671,279,21,37,869,
%T 3444,5696,3444,869,37,65,2728,17558,49872,49872,17558,2728,65,114,
%U 8596,89613,430522,742601,430522,89613,8596,114,200,27004,457188,3713779
%N T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1, 2 or 4 neighboring 1s.
%C Table starts
%C ...1.....2.......4.........7..........12............21..............37
%C ...2....10......28........86.........279...........869............2728
%C ...4....28.....132.......671........3444.........17558...........89613
%C ...7....86.....671......5696.......49872........430522.........3713779
%C ..12...279....3444.....49872......742601......10781621.......157255466
%C ..21...869...17558....430522....10781621.....263456105......6468185511
%C ..37..2728...89613...3713779...157255466....6468185511....267838310277
%C ..65..8596..457188..32095222..2296958734..158971670482..11100574753607
%C .114.27004.2333009.277299810.33523275696.3904685293187.459672982178410
%H R. H. Hardin, <a href="/A296643/b296643.txt">Table of n, a(n) for n = 1..241</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
%F k=2: a(n) = 3*a(n-1) -a(n-2) +6*a(n-3) -6*a(n-4) +6*a(n-5) -5*a(n-6) +3*a(n-7) -a(n-8)
%F k=3: [order 22]
%F k=4: [order 74]
%e Some solutions for n=4 k=4
%e ..0..1..0..0. .1..1..0..0. .1..0..0..1. .0..1..1..1. .0..0..0..1
%e ..0..1..0..1. .1..0..1..1. .1..0..1..0. .1..0..0..0. .1..1..0..1
%e ..0..1..1..0. .0..0..0..1. .1..0..0..0. .1..0..0..1. .0..1..0..0
%e ..1..1..1..0. .1..1..1..0. .1..1..1..0. .1..0..1..0. .0..1..1..0
%Y Column 1 is A005251(n+2).
%Y Column 2 is A296380.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Dec 17 2017