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 A228754 T(n,k)=Number of nXk binary arrays with top left element equal to 1 and no two ones adjacent horizontally or antidiagonally. 12
 1, 1, 2, 2, 3, 4, 3, 9, 8, 8, 5, 20, 39, 21, 16, 8, 50, 126, 168, 55, 32, 13, 119, 482, 780, 723, 144, 64, 21, 289, 1712, 4599, 4808, 3111, 377, 128, 34, 696, 6277, 24246, 43862, 29608, 13386, 987, 256, 55, 1682, 22700, 134440, 342207, 418370, 182288, 57597, 2584, 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....3......9......20........50.........119..........289............696 ...4....8.....39.....126.......482........1712.........6277..........22700 ...8...21....168.....780......4599.......24246.......134440.........728537 ..16...55....723....4808.....43862......342207......2876170.......23326164 ..32..144...3111...29608....418370.....4823826.....61534448......746135864 ..64..377..13386..182288...3990739....67970044...1316714732....23857469157 .128..987..57597.1122240..38067290...957616341..28177227352...762713002760 .256.2584.247827.6908896.363121586.13491214832.602998827928.24382157716612 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) k=4: a(n) = 8*a(n-1) -12*a(n-2) +4*a(n-3) k=5: a(n) = 13*a(n-1) -36*a(n-2) +29*a(n-3) -5*a(n-4) for n>5 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>6 k=7: [order 7] for n>9 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) = 2*a(n-1) +6*a(n-2) -a(n-4) 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..1..0....1..0..0..1....1..0..0..0....1..0..0..1....1..0..1..0 ..0..0..0..1....1..0..0..0....1..0..0..0....0..1..0..0....1..0..0..1 ..0..0..0..0....1..0..0..1....0..0..0..0....0..0..0..1....0..1..0..1 ..0..0..0..1....0..0..0..0....0..1..0..0....0..1..0..0....0..0..0..0 CROSSREFS Column 1 is A000079(n-1) Column 2 is A001906 Column 3 is A095939 Row 1 is A000045 Row 2 is A097075(n+1) Sequence in context: A324480 A164975 A253889 * A171830 A071506 A372645 Adjacent sequences: A228751 A228752 A228753 * A228755 A228756 A228757 KEYWORD nonn,tabl AUTHOR R. H. Hardin Sep 02 2013 STATUS approved

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Last modified July 19 13:41 EDT 2024. Contains 374394 sequences. (Running on oeis4.)