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%I #4 Jan 02 2018 12:00:00
%S 2,3,4,5,8,8,8,29,20,16,13,69,113,51,32,21,200,374,494,132,64,34,552,
%T 1657,2370,2344,341,128,55,1641,6548,17305,16508,10587,883,256,89,
%U 4685,28645,108928,201152,109790,48187,2293,512,144,13716,119531,771393
%N T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 2 or 3 neighboring 1s.
%C Table starts
%C ...2....3.......5........8.........13...........21.............34
%C ...4....8......29.......69........200..........552...........1641
%C ...8...20.....113......374.......1657.........6548..........28645
%C ..16...51.....494.....2370......17305.......108928.........771393
%C ..32..132....2344....16508.....201152......2077060.......25139952
%C ..64..341...10587...109790....2171757.....36084211......715726580
%C .128..883...48187...740555...24145671....659362756....21730243952
%C .256.2293..222804..5099557..273842684..12330890209...681285029028
%C .512.5964.1027173.35164860.3092881435.229556423760.21128576143262
%H R. H. Hardin, <a href="/A297637/b297637.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 4*a(n-1) -3*a(n-2) -4*a(n-4) -a(n-5) +a(n-6)
%F k=3: [order 15]
%F k=4: [order 32]
%F k=5: [order 68]
%F Empirical for row n:
%F n=1: a(n) = a(n-1) +a(n-2)
%F n=2: a(n) = 3*a(n-1) +a(n-2) -a(n-3) +6*a(n-4) -28*a(n-5) -24*a(n-6)
%F n=3: [order 18]
%F n=4: [order 40]
%e Some solutions for n=4 k=4
%e ..1..0..1..0. .0..0..1..0. .1..0..0..1. .1..1..1..0. .1..1..0..0
%e ..1..0..0..0. .0..0..0..0. .0..0..0..0. .0..1..0..0. .0..1..1..0
%e ..1..0..1..0. .0..0..0..0. .0..1..0..0. .0..1..0..0. .1..1..0..0
%e ..1..0..1..0. .0..0..0..1. .0..0..0..0. .1..1..1..0. .1..1..0..1
%Y Column 1 is A000079.
%Y Column 2 is A295346.
%Y Row 1 is A000045(n+2).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 02 2018
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