A263714 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.

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

Offset: 1

Author

R. H. Hardin, Oct 24 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

...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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..618

Formula

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