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 A228660 T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally. 13
 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, 574, 70, 64, 21, 194, 968, 2844, 2228, 2348, 169, 128, 34, 434, 3556, 11148, 24109, 11912, 9598, 408, 256, 55, 1016, 11245, 62368, 128740, 203762, 63688, 39224, 985, 512, 89 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Table starts ...1...1......2.......3.........5..........8...........13............21 ...2...2......8......14........38.........80..........194...........434 ...4...5.....34......78.......335........968.........3556.........11245 ...8..12....140.....416......2844......11148........62368........275708 ..16..29....574....2228.....24109.....128740......1096624.......6780585 ..32..70...2348...11912....203762....1482892.....19236832.....166237206 ..64.169...9598...63688...1720343...17074988....337258048....4073313193 .128.408..39224..340480..14516920..196565912...5910459096...99770848656 .256.985.160282.1820208.122469941.2262692928.103561279328.2443423182349 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 ..1..0..0..1....1..0..0..0....1..0..0..1....1..0..1..0....1..0..0..1 ..1..0..0..0....1..0..1..0....0..0..0..0....1..0..1..0....0..0..0..0 ..0..0..0..0....1..0..1..0....0..0..0..0....1..0..1..0....0..0..1..0 ..0..0..0..0....0..0..0..0....1..0..0..0....0..0..1..0....0..0..0..0 CROSSREFS Column 1 is A000079(n-1) Column 2 is A000129 Row 1 is A000045 Sequence in context: A097986 A210596 A240078 * A228796 A155837 A096445 Adjacent sequences:  A228657 A228658 A228659 * A228661 A228662 A228663 KEYWORD nonn,tabl AUTHOR R. H. Hardin Aug 29 2013 STATUS approved

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Last modified January 28 09:17 EST 2020. Contains 331318 sequences. (Running on oeis4.)