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%I #4 Jan 05 2018 16:01:06
%S 1,2,1,3,5,1,4,19,11,1,6,37,66,24,1,9,71,174,230,55,1,13,237,452,852,
%T 1142,123,1,19,715,2223,3780,5396,4344,276,1,28,1665,9733,28540,34159,
%U 29773,16384,621,1,41,4007,32213,187564,462187,290114,162828,72571,1395
%N T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1, 3 or 4 neighboring 1s.
%C Table starts
%C .1....2......3.......4.........6...........9............13.............19
%C .1....5.....19......37........71.........237...........715...........1665
%C .1...11.....66.....174.......452........2223..........9733..........32213
%C .1...24....230.....852......3780.......28540........187564........1003470
%C .1...55...1142....5396.....34159......462187.......5298077.......43194128
%C .1..123...4344...29773....290114.....6379211.....116064732.....1513886975
%C .1..276..16384..162828...2561262....92963365....2703029494....57155337030
%C .1..621..72571..945314..22815719..1407868835...67944280878..2266768029479
%C .1.1395.287634.5347977.202611948.20923328285.1646896960337.88219789959795
%H R. H. Hardin, <a href="/A297749/b297749.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1) +2*a(n-2) +2*a(n-3) -a(n-5)
%F k=3: [order 14]
%F k=4: [order 40]
%F k=5: [order 77]
%F Empirical for row n:
%F n=1: a(n) = a(n-1) +a(n-3)
%F n=2: a(n) = 2*a(n-1) -a(n-2) +6*a(n-3) +8*a(n-4) -10*a(n-5) -12*a(n-6)
%F n=3: [order 19]
%F n=4: [order 52]
%e Some solutions for n=5 k=4
%e ..1..1..1..0. .0..1..1..0. .0..1..1..0. .1..1..0..0. .0..1..1..1
%e ..1..0..1..0. .0..1..0..1. .0..1..0..1. .0..0..0..0. .0..1..0..1
%e ..0..0..1..0. .0..0..0..1. .0..0..0..0. .0..0..0..0. .0..1..0..1
%e ..1..1..0..0. .0..1..1..1. .1..0..1..0. .1..1..0..0. .0..0..1..1
%e ..0..0..1..0. .0..1..0..0. .0..1..1..0. .0..0..0..0. .0..1..0..0
%Y Column 2 is A295091.
%Y Row 1 is A000930(n+1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jan 05 2018
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