A263764 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 one more element moved upwards than downwards.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 1, 4, 6, 0, 0, 0, 1, 4, 19, 14, 0, 0, 0, 1, 4, 31, 50, 38, 0, 0, 0, 1, 4, 31, 106, 165, 88, 0, 0, 0, 1, 4, 31, 146, 485, 476, 217, 0, 0, 0, 1, 4, 31, 146, 961, 1546, 1543, 506, 0, 0, 0, 1, 4, 31, 146, 1289, 3662, 6083, 4544, 1209, 0, 0, 0, 1

Offset: 1

Author

R. H. Hardin, Oct 25 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...1....1.....1.....1......1......1......1......1......1......1......1......1

.0...2....4.....4.....4......4......4......4......4......4......4......4......4

.0...6...19....31....31.....31.....31.....31.....31.....31.....31.....31.....31

.0..14...50...106...146....146....146....146....146....146....146....146....146

.0..38..165...485...961...1289...1289...1289...1289...1289...1289...1289...1289

.0..88..476..1546..3662...6152...7736...7736...7736...7736...7736...7736...7736

.0.217.1543..6083.18444..41747..68811..85831..85831..85831..85831..85831..85831

.0.506.4544.21020.69848.181272.354568.533302.641302.641302.641302.641302.641302

Examples

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

Links

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

Crossrefs

Diagonal is A179562.