%I #4 Dec 29 2017 07:40:51
%S 2,4,4,8,16,8,16,57,64,16,32,208,393,256,32,64,765,2610,2719,1024,64,
%T 128,2807,17534,33054,18805,4096,128,256,10294,116932,409507,418344,
%U 130063,16384,256,512,37759,780273,4986469,9554038,5294713,899565,65536,512
%N T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 0, 1 or 2 neighboring 1s.
%C Table starts
%C ...2......4........8..........16............32..............64
%C ...4.....16.......57.........208...........765............2807
%C ...8.....64......393........2610.........17534..........116932
%C ..16....256.....2719.......33054........409507.........4986469
%C ..32...1024....18805......418344.......9554038.......211988289
%C ..64...4096...130063.....5294713.....222925151......9012089653
%C .128..16384...899565....67012245....5201484239....383128155296
%C .256..65536..6221735...848136217..121365562862..16287817972455
%C .512.262144.43031893.10734382366.2831807366510.692439110062325
%H R. H. Hardin, <a href="/A297374/b297374.txt">Table of n, a(n) for n = 1..541</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 4*a(n-1)
%F k=3: a(n) = 7*a(n-1) -4*a(n-3)
%F k=4: a(n) = 13*a(n-1) -4*a(n-2) -3*a(n-3) -19*a(n-4) +15*a(n-5) -a(n-6)
%F k=5: [order 9] for n>11
%F k=6: [order 17] for n>19
%F k=7: [order 28] for n>31
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1)
%F n=2: a(n) = 3*a(n-1) +a(n-2) +5*a(n-3) +a(n-4) +a(n-5) -a(n-6) -a(n-7)
%F n=3: [order 12] for n>14
%F n=4: [order 29] for n>31
%F n=5: [order 84] for n>87
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..1..0
%e ..1..0..1..0. .1..0..0..1. .0..0..0..0. .0..1..0..0. .0..0..0..0
%e ..1..0..1..0. .1..0..0..1. .1..0..0..1. .1..0..1..1. .0..1..1..1
%e ..1..0..0..0. .1..0..0..1. .0..1..0..0. .1..0..1..1. .0..0..1..0
%e ..0..0..0..0. .0..0..1..1. .0..1..0..0. .1..0..0..1. .0..0..1..1
%Y Column 1 is A000079.
%Y Column 2 is A000302.
%Y Row 1 is A000079.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 29 2017