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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
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
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.)