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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 three consecutive elements having its maximum within 3 of its minimum.
4

%I #4 Oct 23 2015 20:46:34

%S 1,1,2,1,2,3,1,2,6,5,1,2,6,14,7,1,2,6,24,14,11,1,2,6,24,18,16,16,1,2,

%T 6,24,36,18,22,25,1,2,6,24,36,20,24,36,37,1,2,6,24,36,36,24,40,56,57,

%U 1,2,6,24,36,36,27,40,64,85,85,1,2,6,24,36,36,48,40,64,100,125,130,1,2,6,24,36

%N 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 three consecutive elements having its maximum within 3 of its minimum.

%C Table starts

%C ...1...1...1...1...1...1...1...1...1...1...1...1...1...1...1...1...1...1...1

%C ...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2

%C ...3...6...6...6...6...6...6...6...6...6...6...6...6...6...6...6...6...6...6

%C ...5..14..24..24..24..24..24..24..24..24..24..24..24..24..24..24..24..24..24

%C ...7..14..18..36..36..36..36..36..36..36..36..36..36..36..36..36..36..36..36

%C ..11..16..18..20..36..36..36..36..36..36..36..36..36..36..36..36..36..36..36

%C ..16..22..24..24..27..48..48..48..48..48..48..48..48..48..48..48..48..48..48

%C ..25..36..40..40..40..49..80..80..80..80..80..80..80..80..80..80..80..80..80

%C ..37..56..64..64..64..64..76.128.128.128.128.128.128.128.128.128.128.128.128

%C ..57..85.100.100.100.100.100.120.200.200.200.200.200.200.200.200.200.200.200

%C ..85.125.144.144.144.144.144.144.168.288.288.288.288.288.288.288.288.288.288

%C .130.189.216.216.216.216.216.216.216.256.432.432.432.432.432.432.432.432.432

%C .195.285.324.324.324.324.324.324.324.324.380.648.648.648.648.648.648.648.648

%H R. H. Hardin, <a href="/A263693/b263693.txt">Table of n, a(n) for n = 1..653</a>

%F Empirical for diagonal: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>12

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4)

%F k=2: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>12

%F k=3: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>12

%F k=4: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>12

%F k=5: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>12

%F k=6: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>12

%F k=7: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>13

%e Some solutions for n=7 k=4

%e ..1....0....0....3....1....0....0....0....0....0....0....0....1....0....1....2

%e ..0....2....1....0....0....1....1....1....1....2....1....2....0....1....0....0

%e ..2....1....2....1....3....2....2....2....2....1....2....1....2....2....3....1

%e ..3....3....3....2....2....4....3....4....3....3....4....4....3....4....2....3

%e ..4....4....4....4....4....3....5....5....4....4....3....3....5....5....5....4

%e ..6....5....6....5....5....6....4....6....5....6....5....6....6....3....4....6

%e ..5....6....5....6....6....5....6....3....6....5....6....5....4....6....6....5

%Y Column 1 is A130137(n-1).

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Oct 23 2015