A216800 T(n,k)=Number of permutations of an nXk array with each element moving exactly one horizontally or vertically and without 2-loops.

0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 6, 0, 6, 0, 0, 10, 8, 8, 10, 0, 0, 22, 0, 88, 0, 22, 0, 0, 42, 32, 292, 292, 32, 42, 0, 0, 86, 0, 1774, 0, 1774, 0, 86, 0, 0, 170, 128, 7676, 10140, 10140, 7676, 128, 170, 0, 0, 342, 0, 39844, 0, 207408, 0, 39844, 0, 342, 0, 0, 682, 512, 186996

Offset: 1

Author

R. H. Hardin Sep 17 2012

Keywords

• nonn
• tabl

Comments

Table starts

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

.0....2....2........6........10...........22.............42................86

.0....2....0........8.........0...........32..............0...............128

.0....6....8.......88.......292.........1774...........7676.............39844

.0...10....0......292.........0........10140..............0............361200

.0...22...32.....1774.....10140.......207408........1879040..........27918806

.0...42....0.....7676.........0......1879040..............0.........489300384

.0...86..128....39844....361200.....27918806......489300384.......22902801416

.0..170....0...186996.........0....302667484..............0......539812977524

.0..342..512...927134..12911864...3991662992...129127695440....20296105418276

.0..682....0..4460016.........0..46492284664..............0...550843711073468

.0.1366.2048.21812696.461788640.585384941184.34175930646380.18708387030790218

Examples

			Some solutions for n=4 k=4
..1..5..3..7....1..5..3..7....4..0..1..2....1..5..3..7....4..0..1..2
..0..9..2..6....0..4..2..6....8..6..7..3....0..4..2..6....5..6..7..3
..4.13.11.15....9.13.11.15...12..5..9.10...12..8.14.10...12..8..9.10
..8.12.10.14....8.12.10.14...13.14.15.11...13..9.15.11...13.14.15.11
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..312

Crossrefs

Column 2 is A014113(n-1)

Diagonal is A216678