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 A228683 T(n,k)=Number of nXk binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally. 12
 2, 3, 4, 5, 7, 8, 8, 19, 17, 16, 13, 40, 77, 41, 32, 21, 97, 216, 313, 99, 64, 34, 217, 809, 1152, 1277, 239, 128, 55, 508, 2529, 6737, 6160, 5215, 577, 256, 89, 1159, 8832, 28977, 56549, 32928, 21305, 1393, 512, 144, 2683, 28793, 152048, 333517, 475809, 176032 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ...2....3......5.......8........13.........21...........34............55 ...4....7.....19......40........97........217..........508..........1159 ...8...17.....77.....216.......809.......2529.........8832.........28793 ..16...41....313....1152......6737......28977.......152048........699833 ..32...99...1277....6160.....56549.....333517......2644336......17124415 ..64..239...5215...32928....475809....3837761.....46125216.....419022831 .128..577..21305..176032...4008817...44171841....806190208...10258304689 .256.1393..87049..941056..33795201..508425617..14105294112..251170142257 .512.3363.355685.5030848.284980061.5852202757.246929287360.6150224353031 LINKS R. H. Hardin, Table of n, a(n) for n = 1..1057 FORMULA Empirical for column k: k=1: a(n) = 2*a(n-1) k=2: a(n) = 2*a(n-1) +a(n-2) k=3: a(n) = 5*a(n-1) -3*a(n-2) -3*a(n-3) k=4: a(n) = 6*a(n-1) -2*a(n-2) -8*a(n-3) 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) k=6: [order 7] k=7: [order 12] Empirical for row n: n=1: a(n) = a(n-1) +a(n-2) n=2: a(n) = a(n-1) +3*a(n-2) n=3: a(n) = 2*a(n-1) +6*a(n-2) -5*a(n-3) n=4: a(n) = 2*a(n-1) +16*a(n-2) -7*a(n-3) -18*a(n-4) n=5: [order 7] n=6: [order 10] n=7: [order 16] EXAMPLE Some solutions for n=4 k=4 ..0..0..0..1....1..0..0..0....0..0..1..0....0..0..1..0....1..0..0..0 ..0..1..0..1....1..0..0..0....0..0..1..0....0..0..1..0....1..0..0..0 ..0..0..0..0....0..0..0..1....1..0..1..0....0..0..1..0....1..0..0..0 ..0..0..0..1....0..1..0..1....1..0..0..0....0..0..1..0....0..0..0..0 CROSSREFS Column 1 is A000079 Column 2 is A001333(n+1) Diagonal is A067963 Row 1 is A000045(n+2) Row 2 is A006130(n+1) Sequence in context: A112922 A305077 A302175 * A133017 A290019 A161924 Adjacent sequences:  A228680 A228681 A228682 * A228684 A228685 A228686 KEYWORD nonn,tabl,look AUTHOR R. H. Hardin Aug 30 2013 STATUS approved

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Last modified December 9 08:41 EST 2021. Contains 349627 sequences. (Running on oeis4.)