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

1,3

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000045(n+1)

Sequence in context: A263693 A263714 A263703 * A101161 A245049 A214261

Adjacent sequences: A263749 A263750 A263751 * A263753 A263754 A263755

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 25 2015

Status

approved