%I #4 Apr 08 2018 10:03:00
%S 1,1,2,1,2,4,1,11,2,8,1,13,18,3,16,1,34,8,55,6,32,1,65,44,10,177,10,
%T 64,1,123,56,233,54,474,21,128,1,266,140,123,924,111,1397,42,256,1,
%U 499,364,1518,1096,3875,276,4135,86,512,1,1037,764,2945,8869,5266,17189,1050
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ...1..1.....1....1......1......1........1.........1..........1...........1
%C ...2..2....11...13.....34.....65......123.......266........499........1037
%C ...4..2....18....8.....44.....56......140.......364........764........2352
%C ...8..3....55...10....233....123.....1518......2945......16711.......58462
%C ..16..6...177...54....924...1096.....8869.....29770.....176077......900973
%C ..32.10...474..111...3875...5266....61254....287294....2165323....15547748
%C ..64.21..1397..276..17189..25285...404761...2588958...25019102...250630168
%C .128.42..4135.1050..72529.149381..2822737..26036557..322917567..4472928245
%C .256.86.11882.3589.300519.866961.19107381.258817075.4110999261.79010238897
%H R. H. Hardin, <a href="/A302460/b302460.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F k=3: [order 12]
%F k=4: [order 71] for n>72
%F Empirical for row n:
%F n=1: a(n) = a(n-1)
%F n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
%F n=3: [order 19] for n>20
%F n=4: [order 71] for n>72
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..1..1..1. .0..1..0..1. .0..1..1..0. .0..0..1..0
%e ..0..0..1..1. .1..1..1..0. .0..1..0..1. .0..1..1..1. .0..0..1..0
%e ..0..0..1..1. .1..1..1..1. .0..1..0..1. .1..1..0..1. .1..0..1..0
%e ..1..1..0..0. .0..1..1..1. .0..1..0..1. .0..1..1..1. .0..0..1..0
%e ..1..1..0..0. .1..1..1..0. .0..1..0..1. .0..1..1..0. .0..0..1..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A240513(n-2).
%Y Row 2 is A297870(n+2).
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_, Apr 08 2018