A263693 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.

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, 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, 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

Offset

1,3

Comments

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

...7..14..18..36..36..36..36..36..36..36..36..36..36..36..36..36..36..36..36

..11..16..18..20..36..36..36..36..36..36..36..36..36..36..36..36..36..36..36

..16..22..24..24..27..48..48..48..48..48..48..48..48..48..48..48..48..48..48

..25..36..40..40..40..49..80..80..80..80..80..80..80..80..80..80..80..80..80

..37..56..64..64..64..64..76.128.128.128.128.128.128.128.128.128.128.128.128

..57..85.100.100.100.100.100.120.200.200.200.200.200.200.200.200.200.200.200

..85.125.144.144.144.144.144.144.168.288.288.288.288.288.288.288.288.288.288

.130.189.216.216.216.216.216.216.216.256.432.432.432.432.432.432.432.432.432

.195.285.324.324.324.324.324.324.324.324.380.648.648.648.648.648.648.648.648

Links

R. H. Hardin, Table of n, a(n) for n = 1..653

Formula

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

Empirical for column k:

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

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

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

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

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

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

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

Example

Some solutions for n=7 k=4
..1....0....0....3....1....0....0....0....0....0....0....0....1....0....1....2
..0....2....1....0....0....1....1....1....1....2....1....2....0....1....0....0
..2....1....2....1....3....2....2....2....2....1....2....1....2....2....3....1
..3....3....3....2....2....4....3....4....3....3....4....4....3....4....2....3
..4....4....4....4....4....3....5....5....4....4....3....3....5....5....5....4
..6....5....6....5....5....6....4....6....5....6....5....6....6....3....4....6
..5....6....5....6....6....5....6....3....6....5....6....5....4....6....6....5

Crossrefs

Column 1 is A130137(n-1).

Sequence in context: A249026 A263597 A263905 * A263714 A263703 A263752

Adjacent sequences: A263690 A263691 A263692 * A263694 A263695 A263696

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 23 2015

Status

approved