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A228796
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T(n,k)=Number of nXk binary arrays with top left element equal to 1 and no two ones adjacent horizontally or nw-se.
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13
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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
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..1347
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FORMULA
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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]
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EXAMPLE
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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
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CROSSREFS
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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
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin Sep 04 2013
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STATUS
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approved
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