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A302069
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
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12
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1, 2, 2, 4, 8, 4, 8, 25, 32, 8, 16, 81, 148, 128, 16, 32, 263, 748, 884, 512, 32, 64, 855, 3657, 7070, 5296, 2048, 64, 128, 2778, 18108, 54177, 67070, 31760, 8192, 128, 256, 9027, 89658, 420121, 807601, 636852, 190528, 32768, 256, 512, 29333, 444359
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OFFSET
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1,2
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COMMENTS
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Table starts
...1......2.......4.........8..........16............32..............64
...2......8......25........81.........263...........855............2778
...4.....32.....148.......748........3657.........18108...........89658
...8....128.....884......7070.......54177........420121.........3247765
..16....512....5296.....67070......807601.......9825815.......119508742
..32...2048...31760....636852....12063625.....230634314......4418931065
..64...8192..190528...6048836...180330117....5420105343....163660519064
.128..32768.1143104..57457232..2696254757..127431664603...6065045335103
.256.131072.6858496.545796112.40316943551.2996509042607.224815724811979
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..311
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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) = 4*a(n-1)
k=3: a(n) = 8*a(n-1) -12*a(n-2) for n>3
k=4: a(n) = 16*a(n-1) -76*a(n-2) +148*a(n-3) -124*a(n-4) +36*a(n-5) for n>6
k=5: [order 11] for n>13
k=6: [order 25] for n>27
k=7: [order 53] for n>56
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>6
n=3: [order 15] for n>18
n=4: [order 53] for n>58
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..0. .0..1..0..0. .0..0..1..1. .0..1..1..0. .0..1..0..0
..1..0..0..0. .1..1..1..0. .0..1..0..0. .1..0..1..0. .0..1..1..1
..1..0..1..0. .0..1..1..0. .0..0..1..0. .0..1..0..1. .1..0..1..0
..1..1..1..0. .0..0..1..0. .1..1..1..0. .1..0..1..0. .0..0..1..0
..1..1..0..1. .1..0..1..1. .1..1..0..1. .0..0..0..1. .0..0..1..0
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CROSSREFS
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Column 1 is A000079(n-1).
Column 2 is A004171(n-1).
Row 1 is A000079(n-1).
Row 2 is A301842.
Sequence in context: A299180 A299942 A301841 * A298195 A299089 A299345
Adjacent sequences: A302066 A302067 A302068 * A302070 A302071 A302072
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Mar 31 2018
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STATUS
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approved
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