%I #4 Jan 05 2018 19:00:32

%S 1,1,1,1,2,1,1,12,4,1,1,31,52,7,1,1,78,206,186,14,1,1,225,734,1181,

%T 1045,31,1,1,733,4088,7081,10639,5685,69,1,1,2305,24801,73352,109228,

%U 90727,28565,155,1,1,7156,130159,759243,2263784,1456855,720785,148681,354,1,1

%N T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 4 neighboring 1s.

%C Table starts

%C .1...1......1........1..........1.............1...............1

%C .1...2.....12.......31.........78...........225.............733

%C .1...4.....52......206........734..........4088...........24801

%C .1...7....186.....1181.......7081.........73352..........759243

%C .1..14...1045....10639.....109228.......2263784........45618455

%C .1..31...5685....90727....1456855......59707529......2301783905

%C .1..69..28565...720785...18733087....1504842706....108229776807

%C .1.155.148681..5909241..251641086...39769163381...5394743533114

%C .1.354.783104.48847911.3354939709.1043883771677.267870723932943

%H R. H. Hardin, <a href="/A297762/b297762.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

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

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

%F k=3: [order 15]

%F k=4: [order 33]

%F k=5: [order 78]

%F Empirical for row n:

%F n=1: a(n) = a(n-1)

%F n=2: a(n) = 4*a(n-1) -3*a(n-2) +a(n-3) +6*a(n-4) -18*a(n-5)

%F n=3: [order 20]

%F n=4: [order 52]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A202973.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 05 2018