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A228390 T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally or vertically.

%I A228390 #7 Sep 01 2013 18:29:13
%S A228390 1,1,1,2,2,2,3,5,5,3,5,12,21,12,5,8,29,72,72,29,8,13,70,268,382,268,
%T A228390 70,13,21,169,963,2104,2104,963,169,21,34,408,3513,11449,17578,11449,
%U A228390 3513,408,34,55,985,12732,62546,143072,143072,62546,12732,985,55,89,2378
%N A228390 T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally or vertically.
%C A228390 Table starts
%C A228390 ..1...1.....2.......3........5..........8...........13............21
%C A228390 ..1...2.....5......12.......29.........70..........169...........408
%C A228390 ..2...5....21......72......268........963.........3513.........12732
%C A228390 ..3..12....72.....382.....2104......11449........62546........341249
%C A228390 ..5..29...268....2104....17578.....143072......1177709.......9646285
%C A228390 ..8..70...963...11449...143072....1755243.....21683149.....267157140
%C A228390 .13.169..3513...62546..1177709...21683149....402968942....7458864720
%C A228390 .21.408.12732..341249..9646285..267157140...7458864720..207573951234
%C A228390 .34.985.46274.1862631.79185086.3294926929.138305554175.5784184947686
%H A228390 R. H. Hardin, <a href="/A228390/b228390.txt">Table of n, a(n) for n = 1..1860</a>
%F A228390 Empirical for column k:
%F A228390 k=1: a(n) = a(n-1) +a(n-2)
%F A228390 k=2: a(n) = 2*a(n-1) +a(n-2)
%F A228390 k=3: a(n) = 2*a(n-1) +6*a(n-2) -a(n-4)
%F A228390 k=4: a(n) = 4*a(n-1) +9*a(n-2) -5*a(n-3) -4*a(n-4) +a(n-5)
%F A228390 k=5: [order 9]
%F A228390 k=6: [order 11]
%F A228390 k=7: [order 21]
%e A228390 Some solutions for n=4 k=4
%e A228390 ..1..0..1..0....1..0..1..0....1..0..1..0....1..0..1..0....1..0..1..0
%e A228390 ..0..0..0..1....0..0..0..0....0..0..0..1....0..1..0..1....0..0..0..0
%e A228390 ..1..0..1..0....0..0..0..0....1..0..0..0....0..0..1..0....1..0..0..0
%e A228390 ..0..1..0..0....0..1..0..1....0..1..0..1....0..0..0..0....0..0..0..1
%Y A228390 Column 1 is A000045
%Y A228390 Column 2 is A000129
%K A228390 nonn,tabl
%O A228390 1,4
%A A228390 _R. H. Hardin_ Aug 21 2013