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A222334
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T(n,k)=Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..k array extended with zeros and convolved with 1,1
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6
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2, 2, 3, 2, 3, 4, 2, 3, 4, 6, 2, 3, 4, 7, 9, 2, 3, 4, 7, 11, 13, 2, 3, 4, 7, 11, 17, 19, 2, 3, 4, 7, 11, 18, 27, 28, 2, 3, 4, 7, 11, 18, 29, 42, 41, 2, 3, 4, 7, 11, 18, 29, 46, 66, 60, 2, 3, 4, 7, 11, 18, 29, 47, 74, 104, 88, 2, 3, 4, 7, 11, 18, 29, 47, 76, 118, 163, 129, 2, 3, 4, 7, 11, 18, 29, 47
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OFFSET
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1,1
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COMMENTS
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Table starts
....2....2.....2.....2.....2.....2.....2.....2.....2.....2.....2
....3....3.....3.....3.....3.....3.....3.....3.....3.....3.....3
....4....4.....4.....4.....4.....4.....4.....4.....4.....4.....4
....6....7.....7.....7.....7.....7.....7.....7.....7.....7.....7
....9...11....11....11....11....11....11....11....11....11....11
...13...17....18....18....18....18....18....18....18....18....18
...19...27....29....29....29....29....29....29....29....29....29
...28...42....46....47....47....47....47....47....47....47....47
...41...66....74....76....76....76....76....76....76....76....76
...60..104...118...122...123...123...123...123...123...123...123
...88..163...189...197...199...199...199...199...199...199...199
..129..256...303...317...321...322...322...322...322...322...322
..189..402...485...511...519...521...521...521...521...521...521
..277..631...777...824...838...842...843...843...843...843...843
..406..991..1244..1328..1354..1362..1364..1364..1364..1364..1364
..595.1556..1992..2141..2188..2202..2206..2207..2207..2207..2207
..872.2443..3190..3451..3535..3561..3569..3571..3571..3571..3571
.1278.3836..5108..5563..5712..5759..5773..5777..5778..5778..5778
.1873.6023..8180..8967..9229..9313..9339..9347..9349..9349..9349
.2745.9457.13099.14454.14912.15061.15108.15122.15126.15127.15127
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)+a(n-3)
k=2: a(n) = a(n-1)+a(n-3)+a(n-5)
k=3: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)
k=4: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)
k=5: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)+a(n-11)
k=6: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)+a(n-11)+a(n-13)
k=7: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)+a(n-11)+a(n-13)+a(n-15)
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EXAMPLE
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Some solutions for n=6 k=4, one extended zero followed by filtered positions
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....1....0....1....0....1....0....1....0....0....1....0....1....0....0
..0....0....0....1....0....0....0....1....0....0....0....0....0....0....1....1
..0....1....1....0....0....1....0....0....1....0....0....0....1....0....0....0
..0....0....0....0....0....0....0....0....0....1....0....0....0....1....1....0
..0....1....0....0....1....0....0....1....1....0....1....0....0....0....0....0
..1....0....0....1....0....1....1....0....0....0....0....0....0....0....0....0
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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