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

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

...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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000045(n+1).

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