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

Author

R. H. Hardin, Oct 23 2015

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A130137(n-1).

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