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 A228796 T(n,k)=Number of nXk binary arrays with top left element equal to 1 and no two ones adjacent horizontally or nw-se. 13
 1, 1, 2, 2, 2, 4, 3, 8, 5, 8, 5, 16, 36, 13, 16, 8, 42, 97, 156, 34, 32, 13, 98, 411, 586, 672, 89, 64, 21, 240, 1394, 3957, 3588, 2892, 233, 128, 34, 576, 5223, 19474, 37944, 22060, 12444, 610, 256, 55, 1394, 18708, 111966, 272952, 362511, 135768, 53544, 1597, 512 (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......16........42..........98..........240............576 ...4....5.....36......97.......411........1394.........5223..........18708 ...8...13....156.....586......3957.......19474.......111966.........596273 ..16...34....672....3588.....37944......272952......2404290.......19027372 ..32...89...2892...22060....362511.....3835792.....51557716......607251543 ..64..233..12444..135768...3459357....53992646...1104367784....19393508581 .128..610..53544..835776..33001836...760460212..23641626212...619684261316 .256.1597.230388.5145232.314810115.10712702564.505993241296.19806136078115 LINKS R. H. Hardin, Table of n, a(n) for n = 1..1347 FORMULA Empirical for column k: k=1: a(n) = 2*a(n-1) k=2: a(n) = 3*a(n-1) -a(n-2) k=3: a(n) = 5*a(n-1) -3*a(n-2) for n>3 k=4: a(n) = 8*a(n-1) -12*a(n-2) +4*a(n-3) for n>4 k=5: a(n) = 13*a(n-1) -36*a(n-2) +29*a(n-3) -5*a(n-4) for n>6 k=6: a(n) = 21*a(n-1) -112*a(n-2) +217*a(n-3) -157*a(n-4) +36*a(n-5) for n>7 k=7: [order 7] for n>10 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) +a(n-3) n=3: a(n) = a(n-1) +8*a(n-2) +6*a(n-3) -a(n-4) -a(n-5) n=4: [order 8] n=5: [order 13] n=6: [order 21] n=7: [order 34] EXAMPLE Some solutions for n=4 k=4 ..1..0..0..1....1..0..1..0....1..0..0..1....1..0..0..0....1..0..0..1 ..0..0..0..1....1..0..1..0....0..0..1..0....1..0..1..0....1..0..0..1 ..0..1..0..1....1..0..0..0....0..0..1..0....0..0..0..0....1..0..0..0 ..0..1..0..1....1..0..1..0....1..0..1..0....0..0..0..0....1..0..0..0 CROSSREFS Column 1 is A000079(n-1) Column 2 is A001519 Row 1 is A000045 Sequence in context: A240078 A344789 A228660 * A155837 A096445 A125915 Adjacent sequences: A228793 A228794 A228795 * A228797 A228798 A228799 KEYWORD nonn,tabl AUTHOR R. H. Hardin Sep 04 2013 STATUS approved

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Last modified March 31 00:51 EDT 2023. Contains 361623 sequences. (Running on oeis4.)