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A263714
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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 every four consecutive elements having its maximum within 4 of its minimum
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6
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1, 1, 2, 1, 2, 3, 1, 2, 6, 5, 1, 2, 6, 14, 8, 1, 2, 6, 24, 31, 11, 1, 2, 6, 24, 78, 34, 17, 1, 2, 6, 24, 120, 60, 39, 25, 1, 2, 6, 24, 120, 72, 50, 46, 37, 1, 2, 6, 24, 120, 144, 54, 52, 64, 57, 1, 2, 6, 24, 120, 144, 60, 54, 70, 104, 84, 1, 2, 6, 24, 120, 144, 108, 54, 72, 116, 161, 127, 1
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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...1...1...1...1...1
...2...2...2...2...2...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...6...6...6...6...6
...5..14..24..24..24..24..24..24..24..24..24..24..24..24..24..24..24..24..24
...8..31..78.120.120.120.120.120.120.120.120.120.120.120.120.120.120.120.120
..11..34..60..72.144.144.144.144.144.144.144.144.144.144.144.144.144.144.144
..17..39..50..54..60.108.108.108.108.108.108.108.108.108.108.108.108.108.108
..25..46..52..54..54..60.108.108.108.108.108.108.108.108.108.108.108.108.108
..37..64..70..72..72..72..81.144.144.144.144.144.144.144.144.144.144.144.144
..57.104.116.120.120.120.120.147.240.240.240.240.240.240.240.240.240.240.240
..84.161.184.192.192.192.192.192.228.384.384.384.384.384.384.384.384.384.384
.127.249.292.308.308.308.308.308.308.368.616.616.616.616.616.616.616.616.616
.191.385.449.480.480.480.480.480.480.480.576.960.960.960.960.960.960.960.960
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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) -a(n-4) +2*a(n-5) -a(n-6) +a(n-7)
k=2: a(n) = a(n-1) +a(n-3) -a(n-4) +2*a(n-5) -a(n-6) +a(n-7) for n>18
k=3: a(n) = a(n-1) +a(n-3) -a(n-4) +2*a(n-5) -a(n-6) +a(n-7) for n>18
k=4: a(n) = a(n-1) +a(n-3) -a(n-4) +2*a(n-5) -a(n-6) +a(n-7) for n>18
k=5: a(n) = a(n-1) +a(n-3) -a(n-4) +2*a(n-5) -a(n-6) +a(n-7) for n>18
k=6: a(n) = a(n-1) +a(n-3) -a(n-4) +2*a(n-5) -a(n-6) +a(n-7) for n>18
k=7: a(n) = a(n-1) +a(n-3) -a(n-4) +2*a(n-5) -a(n-6) +a(n-7) for n>18
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EXAMPLE
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Some solutions for n=7 k=4
..0....0....1....0....0....0....0....3....1....0....0....0....0....1....1....0
..1....1....0....1....4....1....1....0....0....1....2....1....1....0....0....1
..3....3....3....2....1....3....2....1....3....3....1....2....3....4....4....4
..4....2....4....3....3....4....4....4....2....2....4....3....2....2....3....2
..2....5....2....5....5....5....5....2....4....4....3....4....4....3....2....3
..5....4....5....6....2....6....3....5....5....5....5....5....6....5....5....5
..6....6....6....4....6....2....6....6....6....6....6....6....5....6....6....6
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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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