A263787 T(n,k) = Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and exactly two more elements moved upwards than downwards.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 5, 10, 3, 0, 0, 0, 0, 1, 5, 37, 31, 11, 0, 0, 0, 0, 1, 5, 66, 116, 134, 31, 0, 0, 0, 0, 1, 5, 66, 267, 572, 439, 93, 0, 0, 0, 0, 1, 5, 66, 392, 1721, 2042, 1604, 248, 0, 0, 0, 0, 1, 5, 66, 392, 3522

Offset

1,26

Comments

Table starts

.0...0.....0......0......0.......0.......0........0........0........0........0

.0...0.....0......0......0.......0.......0........0........0........0........0

.0...0.....0......0......0.......0.......0........0........0........0........0

.0...0.....1......1......1.......1.......1........1........1........1........1

.0...0.....2......5......5.......5.......5........5........5........5........5

.0...1....10.....37.....66......66......66.......66.......66.......66.......66

.0...3....31....116....267.....392.....392......392......392......392......392

.0..11...134....572...1721....3522....4859.....4859.....4859.....4859.....4859

.0..31...439...2042...6618...15699...26994....34659....34659....34659....34659

.0..93..1604...9298..35203..104014..232208...383663...482272...482272...482272

.0.248..5088..35064.144762..463811.1161998..2245936..3388097..4099634..4099634

.0.670.17115.149613.741173.2735525.8246455.19777342.37109391.54900952.65762489

Links

R. H. Hardin, Table of n, a(n) for n = 1..424

Example

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

Crossrefs

Diagonal is A169934.

Sequence in context: A017857 A127842 A127512 * A307710 A112207 A112208

Adjacent sequences: A263784 A263785 A263786 * A263788 A263789 A263790

Keyword

nonn,tabl,changed

Author

R. H. Hardin, Oct 26 2015

Status

approved