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A263597
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T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and the median of every three consecutive elements nondecreasing.
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7
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1, 1, 2, 1, 2, 3, 1, 2, 6, 5, 1, 2, 6, 12, 8, 1, 2, 6, 16, 25, 13, 1, 2, 6, 16, 41, 57, 21, 1, 2, 6, 16, 52, 108, 124, 34, 1, 2, 6, 16, 52, 164, 280, 268, 55, 1, 2, 6, 16, 52, 208, 476, 729, 588, 89, 1, 2, 6, 16, 52, 208, 676, 1428, 1908, 1285, 144, 1, 2, 6, 16, 52, 208, 800, 2208, 4308
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OFFSET
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1,3
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COMMENTS
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Table starts
..1....1....1.....1.....1.....1.....1.....1.....1.....1.....1.....1.....1.....1
..2....2....2.....2.....2.....2.....2.....2.....2.....2.....2.....2.....2.....2
..3....6....6.....6.....6.....6.....6.....6.....6.....6.....6.....6.....6.....6
..5...12...16....16....16....16....16....16....16....16....16....16....16....16
..8...25...41....52....52....52....52....52....52....52....52....52....52....52
.13...57..108...164...208...208...208...208...208...208...208...208...208...208
.21..124..280...476...676...800...800...800...800...800...800...800...800...800
.34..268..729..1428..2208..2900..3360..3360..3360..3360..3360..3360..3360..3360
.55..588.1908..4308..7696.10960.14024.16224.16224.16224.16224.16224.16224.16224
.89.1285.4969.12816.25508.40792.55492.69212.78088.78088.78088.78088.78088.78088
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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-2)
k=2: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4)
k=3: a(n) = a(n-1) +a(n-2) +7*a(n-3) +2*a(n-4) +4*a(n-5) -a(n-7) -a(n-8)
k=4: [order 15]
k=5: [order 31]
k=6: [order 67]
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EXAMPLE
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Some solutions for n=6 k=4
..1....1....1....0....2....0....0....0....1....4....3....2....1....4....0....2
..2....2....0....1....1....5....3....1....5....1....1....0....4....0....1....0
..3....3....2....3....5....2....2....2....0....0....0....1....0....1....3....1
..0....0....4....4....3....3....1....5....2....2....2....5....3....3....5....3
..4....5....3....2....0....4....4....3....4....3....4....3....5....2....2....4
..5....4....5....5....4....1....5....4....3....5....5....4....2....5....4....5
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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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