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

Author

R. H. Hardin, Oct 25 2015

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000045(n+1)

Diagonal is A062868