A263703 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 4 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, 56, 21, 1, 2, 6, 24, 120, 110, 104, 34, 1, 2, 6, 24, 120, 168, 169, 208, 55, 1, 2, 6, 24, 120, 288, 204, 301, 418, 89, 1, 2, 6, 24, 120, 288, 276, 348, 616, 873, 144, 1, 2, 6, 24, 120, 288, 456, 374

Offset

1,3

Comments

Table starts

...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

...3....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

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

..13...56...110...168...288...288...288...288...288...288...288...288...288

..21..104...169...204...276...456...456...456...456...456...456...456...456

..34..208...301...348...374...488...768...768...768...768...768...768...768

..55..418...616...696...732...754..1002..1508..1508..1508..1508..1508..1508

..89..873..1373..1601..1673..1699..1759..2393..3434..3434..3434..3434..3434

.144.1772..2908..3476..3692..3744..3766..3906..5238..7560..7560..7560..7560

.233.3545..5908..7244..7784..7940..7984..7999..8312.11107.16024.16024.16024

.377.7103.11544.14048.15360.15748.15880.15908.15930.16548.21922.31872.31872

Links

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

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +a(n-2) +7*a(n-5) +2*a(n-6) +a(n-7) +5*a(n-8) -4*a(n-9) -3*a(n-10) -3*a(n-11) -4*a(n-12) -4*a(n-14) -a(n-15) +3*a(n-16) -a(n-17) +a(n-19)

k=3: [same order 19] for n>27

k=4: [same order 19] for n>27

k=5: [same order 19] for n>29

k=6: [same order 19] for n>31

k=7: [same order 19] for n>33

Example

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

Crossrefs

Column 1 is A000045(n+1).

Sequence in context: A263905 A263693 A263714 * A263752 A101161 A245049

Adjacent sequences: A263700 A263701 A263702 * A263704 A263705 A263706

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 24 2015

Status

approved