A263939 T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and the total absolute value of displacements not greater than n.

1, 1, 2, 1, 2, 3, 1, 2, 3, 5, 1, 2, 3, 11, 8, 1, 2, 3, 11, 17, 13, 1, 2, 3, 11, 17, 49, 21, 1, 2, 3, 11, 17, 70, 80, 34, 1, 2, 3, 11, 17, 70, 108, 249, 55, 1, 2, 3, 11, 17, 70, 108, 423, 414, 89, 1, 2, 3, 11, 17, 70, 108, 483, 664, 1237, 144, 1, 2, 3, 11, 17, 70, 108, 483, 739, 2667

Offset

1,3

Comments

Table starts

...1.....1......1......1......1......1......1......1......1......1......1

...2.....2......2......2......2......2......2......2......2......2......2

...3.....3......3......3......3......3......3......3......3......3......3

...5....11.....11.....11.....11.....11.....11.....11.....11.....11.....11

...8....17.....17.....17.....17.....17.....17.....17.....17.....17.....17

..13....49.....70.....70.....70.....70.....70.....70.....70.....70.....70

..21....80....108....108....108....108....108....108....108....108....108

..34...249....423....483....483....483....483....483....483....483....483

..55...414....664....739....739....739....739....739....739....739....739

..89..1237...2667...3271...3426...3426...3426...3426...3426...3426...3426

.144..2099...4221...5030...5216...5216...5216...5216...5216...5216...5216

.233..6314..17124..22666..24476..24854..24854..24854..24854..24854..24854

.377.10846..27252..34917..37233..37674..37674..37674..37674..37674..37674

.610.32254.110935.158899.176887.181883.182772.182772.182772.182772.182772

.987.56036.177405.245151.268945.275132.276148.276148.276148.276148.276148

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)

Example

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

Crossrefs

Column 1 is A000045(n+1).

Sequence in context: A264482 A193588 A165884 * A347499 A136311 A243884

Adjacent sequences: A263936 A263937 A263938 * A263940 A263941 A263942

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 30 2015

Status

approved