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A281080 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than two of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards. 8

%I

%S 0,0,0,0,0,0,0,6,6,0,0,24,55,24,0,0,92,244,244,92,0,0,318,894,958,894,

%T 318,0,0,1056,2948,3330,3330,2948,1056,0,0,3406,9188,10474,10954,

%U 10474,9188,3406,0,0,10770,27580,30808,32244,32244,30808,27580,10770,0,0,33542

%N T(n,k)=Number of nXk 0..1 arrays with no element equal to more than two of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%C Table starts

%C .0.....0......0......0.......0.......0.......0........0........0........0

%C .0.....0......6.....24......92.....318....1056.....3406....10770....33542

%C .0.....6.....55....244.....894....2948....9188....27580....80579...230740

%C .0....24....244....958....3330...10474...30808....86860...237624...636256

%C .0....92....894...3330...10954...32244...89147...236332...609693..1542674

%C .0...318...2948..10474...32244...89042..231146...578810..1415986..3412832

%C .0..1056...9188..30808...89147..231146..566178..1343304..3132736..7230554

%C .0..3406..27580..86860..236332..578810.1343304..3035844..6776640.15052898

%C .0.10770..80579.237624..609693.1415986.3132736..6776640.14551996.31239986

%C .0.33542.230740.636256.1542674.3412832.7230554.15052898.31239986.65113158

%H R. H. Hardin, <a href="/A281080/b281080.txt">Table of n, a(n) for n = 1..363</a>

%F Empirical for column k:

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

%F k=2: [order 12]

%F k=3: [order 12] for n>16

%F k=4: [order 19] for n>25

%F k=5: [order 25] for n>32

%F k=6: [order 29] for n>37

%F k=7: [order 33] for n>42

%e Some solutions for n=4 k=4

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

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

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

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

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Jan 14 2017

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Last modified May 22 12:28 EDT 2022. Contains 353950 sequences. (Running on oeis4.)