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

Author

R. H. Hardin, Oct 26 2015

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Diagonal is A169934.