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%I #7 Sep 02 2013 02:47:30
%S 1,1,2,2,2,4,3,8,5,8,5,14,34,12,16,8,38,78,140,29,32,13,80,335,416,
%T 574,70,64,21,194,968,2844,2228,2348,169,128,34,434,3556,11148,24109,
%U 11912,9598,408,256,55,1016,11245,62368,128740,203762,63688,39224,985,512,89
%N T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.
%C Table starts
%C ...1...1......2.......3.........5..........8...........13............21
%C ...2...2......8......14........38.........80..........194...........434
%C ...4...5.....34......78.......335........968.........3556.........11245
%C ...8..12....140.....416......2844......11148........62368........275708
%C ..16..29....574....2228.....24109.....128740......1096624.......6780585
%C ..32..70...2348...11912....203762....1482892.....19236832.....166237206
%C ..64.169...9598...63688...1720343...17074988....337258048....4073313193
%C .128.408..39224..340480..14516920..196565912...5910459096...99770848656
%C .256.985.160282.1820208.122469941.2262692928.103561279328.2443423182349
%H R. H. Hardin, <a href="/A228660/b228660.txt">Table of n, a(n) for n = 1..1057</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 2*a(n-1) +a(n-2)
%F k=3: a(n) = 5*a(n-1) -3*a(n-2) -3*a(n-3)
%F k=4: a(n) = 6*a(n-1) -2*a(n-2) -8*a(n-3)
%F k=5: a(n) = 12*a(n-1) -27*a(n-2) -32*a(n-3) +49*a(n-4) +20*a(n-5) -5*a(n-6)
%F k=6: [order 7]
%F k=7: [order 12]
%F Empirical for row n:
%F n=1: a(n) = a(n-1) +a(n-2)
%F n=2: a(n) = a(n-1) +3*a(n-2)
%F n=3: a(n) = 2*a(n-1) +6*a(n-2) -5*a(n-3)
%F n=4: a(n) = 2*a(n-1) +16*a(n-2) -7*a(n-3) -18*a(n-4)
%F n=5: [order 7]
%F n=6: [order 10]
%F n=7: [order 16]
%e Some solutions for n=4 k=4
%e ..1..0..0..1....1..0..0..0....1..0..0..1....1..0..1..0....1..0..0..1
%e ..1..0..0..0....1..0..1..0....0..0..0..0....1..0..1..0....0..0..0..0
%e ..0..0..0..0....1..0..1..0....0..0..0..0....1..0..1..0....0..0..1..0
%e ..0..0..0..0....0..0..0..0....1..0..0..0....0..0..1..0....0..0..0..0
%Y Column 1 is A000079(n-1)
%Y Column 2 is A000129
%Y Row 1 is A000045
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_ Aug 29 2013
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