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A280902
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T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
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11
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0, 0, 0, 0, 1, 0, 1, 10, 9, 0, 2, 213, 646, 124, 0, 9, 2292, 22568, 22632, 1464, 0, 34, 21762, 492490, 1451655, 610448, 15768, 0, 124, 184076, 9426050, 65348136, 75809243, 14262832, 159920, 0, 432, 1457827, 162640161, 2571528867, 7083739466
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OFFSET
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1,8
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COMMENTS
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Table starts
.0........0............0...............1..................2...................9
.0........1...........10.............213...............2292...............21762
.0........9..........646...........22568.............492490.............9426050
.0......124........22632.........1451655...........65348136..........2571528867
.0.....1464.......610448........75809243.........7083739466........574982226478
.0....15768.....14262832......3521886844.......684011230518.....114677717497532
.0...159920....304584096....151803173493.....61277484218852...21239418911643829
.0..1554304...6117000704...6210239609889...5208435552362140.3734730743379447607
.0.14632704.117496694272.244458357395448.425813044528570428
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..96
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: [order 6] for n>8
k=3: [order 6] for n>8
k=4: [order 12] for n>14
k=5: [order 24] for n>27
Empirical for row n:
n=1: a(n) = 6*a(n-1) -6*a(n-2) -16*a(n-3) +12*a(n-4) +24*a(n-5) +8*a(n-6) for n>10
n=2: [order 15] for n>17
n=3: [order 54] for n>60
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EXAMPLE
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Some solutions for n=3 k=4
..0..0..1..2. .0..0..1..0. .0..1..0..0. .0..1..0..2. .0..1..2..0
..1..1..2..1. .2..1..0..0. .2..1..0..2. .1..2..2..0. .1..1..1..2
..0..0..1..1. .1..0..2..0. .1..0..2..0. .1..1..1..2. .2..2..0..1
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CROSSREFS
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Row 1 is A280309.
Sequence in context: A317813 A038310 A318421 * A118768 A318255 A008956
Adjacent sequences: A280899 A280900 A280901 * A280903 A280904 A280905
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Jan 10 2017
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STATUS
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approved
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