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A297374 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 0, 1 or 2 neighboring 1s. 13

%I

%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

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Last modified February 18 21:20 EST 2020. Contains 332028 sequences. (Running on oeis4.)