A263752 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 5 of its minimum.

1, 1, 2, 1, 2, 3, 1, 2, 6, 5, 1, 2, 6, 14, 8, 1, 2, 6, 24, 31, 13, 1, 2, 6, 24, 78, 73, 21, 1, 2, 6, 24, 120, 230, 160, 34, 1, 2, 6, 24, 120, 504, 506, 357, 55, 1, 2, 6, 24, 120, 720, 930, 1128, 814, 89, 1, 2, 6, 24, 120, 720, 1560, 1794, 2641, 1836, 144, 1, 2, 6, 24, 120, 720, 2400

Offset: 1

Author

R. H. Hardin, Oct 25 2015

Keywords

• nonn
• tabl

Comments

Table starts

..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

..3....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

..8...31...78..120...120...120...120...120...120...120...120...120...120...120

.13...73..230..504...720...720...720...720...720...720...720...720...720...720

.21..160..506..930..1560..2400..2400..2400..2400..2400..2400..2400..2400..2400

.34..357.1128.1794..2352..3552..5424..5424..5424..5424..5424..5424..5424..5424

.55..814.2641.3852..4704..5484..7872.11568.11568.11568.11568.11568.11568.11568

.89.1836.6655.9246.10946.12058.13426.18918.26796.26796.26796.26796.26796.26796

Examples

			Some solutions for n=10 k=4
..0....4....1....0....1....0....0....0....0....4....1....3....1....2....0....0
..1....1....3....2....0....3....2....5....1....0....3....5....3....0....5....1
..2....0....2....1....2....2....1....1....3....2....2....4....0....1....1....3
..3....3....0....3....4....1....3....6....2....1....0....0....2....4....2....2
..5....2....4....4....3....4....4....2....4....3....4....1....4....5....3....7
..8....5....5....7....5....6....5....3....7....5....5....2....7....3....7....5
..4....6....6....9....6....7....8....4....9....6....8....6....8....6....4....4
..9....7....9....6....7....8....7....7....6....9....7....7....6....7....8....6
..6....8....7....5....9....5....9....8....5....7....6....8....5....9....6....9
..7....9....8....8....8....9....6....9....8....8....9....9....9....8....9....8
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..652

Crossrefs

Column 1 is A000045(n+1)

Formula

Empirical for column k:

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

k=2: [order 13]

k=3: [order 62]

k=4: [same order 62] for n>74

k=5: [same order 62] for n>74

k=6: [same order 62] for n>76

k=7: [same order 62] for n>78