A263744 T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and equal numbers of elements moved upwards and downwards

1, 1, 2, 1, 2, 3, 1, 2, 4, 5, 1, 2, 4, 10, 8, 1, 2, 4, 14, 19, 13, 1, 2, 4, 14, 36, 43, 21, 1, 2, 4, 14, 46, 110, 90, 34, 1, 2, 4, 14, 46, 214, 277, 202, 55, 1, 2, 4, 14, 46, 282, 664, 823, 434, 89, 1, 2, 4, 14, 46, 282, 1118, 2516, 2292, 971, 144, 1, 2, 4, 14, 46, 282, 1394, 5962

Offset

1,3

Comments

Table starts

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

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

..3...4....4.....4......4......4......4......4......4......4......4......4

..5..10...14....14.....14.....14.....14.....14.....14.....14.....14.....14

..8..19...36....46.....46.....46.....46.....46.....46.....46.....46.....46

.13..43..110...214....282....282....282....282....282....282....282....282

.21..90..277...664...1118...1394...1394...1394...1394...1394...1394...1394

.34.202..823..2516...5962..10090..12658..12658..12658..12658..12658..12658

.55.434.2292..7989..21974..44914..68834..83122..83122..83122..83122..83122

.89.971.6862.30299.100324.266476.535262.816882.985730.985730.985730.985730

Links

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

Example

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

Crossrefs

Column 1 is A000045(n+1)

Diagonal is A062868

Sequence in context: A210950 A214314 A209435 * A268956 A208515 A286880

Adjacent sequences: A263741 A263742 A263743 * A263745 A263746 A263747

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 25 2015

Status

approved