%I #4 Apr 17 2018 13:11:47
%S 1,2,2,4,8,4,8,20,25,8,16,52,68,81,16,32,136,187,308,264,32,64,360,
%T 579,1047,1320,857,64,128,960,1797,4237,5299,5220,2785,128,256,2576,
%U 5571,18513,27719,24030,22652,9050,256,512,6944,17382,79945,166978,160253
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ...1.....2......4.......8.......16........32..........64..........128
%C ...2.....8.....20......52......136.......360.........960.........2576
%C ...4....25.....68.....187......579......1797........5571........17382
%C ...8....81....308....1047.....4237.....18513.......79945.......344190
%C ..16...264...1320....5299....27719....166978......970892......5570473
%C ..32...857...5220...24030...160253...1298140.....9976891.....75234550
%C ..64..2785..22652..123538..1044810..11644063...121524556...1219773362
%C .128..9050..95220..612923..6647878.101648313..1423906011..18974341664
%C .256.29407.390580.2935811.40950485.858924912.16163776349.285987277414
%H R. H. Hardin, <a href="/A303016/b303016.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
%F k=3: [order 10]
%F k=4: [order 43] for n>44
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1)
%F n=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3) for n>4
%F n=3: [order 15] for n>16
%F n=4: [order 62] for n>64
%e Some solutions for n=5 k=4
%e ..0..0..0..1. .0..0..0..1. .0..1..0..1. .0..1..1..0. .0..1..0..1
%e ..0..1..0..1. .1..1..1..1. .1..1..0..1. .0..0..1..1. .0..0..0..1
%e ..0..1..0..0. .0..0..0..1. .0..0..0..1. .0..0..0..0. .1..0..1..1
%e ..0..1..1..0. .1..1..1..1. .1..1..0..1. .1..1..0..0. .0..1..0..1
%e ..0..1..0..1. .0..1..0..0. .1..1..0..1. .0..1..1..0. .0..1..0..1
%Y Column 1 is A000079(n-1).
%Y Column 2 is A240478.
%Y Row 1 is A000079(n-1).
%Y Row 2 is A302323.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Apr 17 2018