A181206 T(n,k) = number of n X k matrices containing a permutation of 1..n*k moving each element at most to a neighboring position.

1, 2, 2, 3, 9, 3, 5, 32, 32, 5, 8, 121, 229, 121, 8, 13, 450, 1845, 1845, 450, 13, 21, 1681, 14320, 32000, 14320, 1681, 21, 34, 6272, 112485, 535229, 535229, 112485, 6272, 34, 55, 23409, 880163, 9049169, 19114420, 9049169, 880163, 23409, 55, 89, 87362

Offset: 1

Author

R. H. Hardin, Oct 10 2010

Keywords

• nonn
• tabl

Comments

Also, the number of perfect matchings in the graph P_2 X P_k X P_n. - Andrew Howroyd, May 17 2017

Examples

			Table starts:
..1......2.........3............5................8..................13
..2......9........32..........121..............450................1681
..3.....32.......229.........1845............14320..............112485
..5....121......1845........32000...........535229.............9049169
..8....450.....14320.......535229.........19114420...........692276437
.13...1681....112485......9049169........692276437.........53786626921
.21...6272....880163....152526845......24972353440.......4161756233501
.34..23409...6895792...2573281769.....901990734650.....322462050747008
.55..87362..54003765..43402320448...32567565264292...24976513162427653
.89.326041.422983905.732106008249.1176040842289105.1934824269280528177
...
All solutions for 3X2
..1..2....1..2....1..2....1..2....1..2....1..2....1..2....1..2....1..2....1..4
..3..4....4..3....4..3....4..6....3..4....3..6....5..4....5..3....5..6....3..2
..5..6....5..6....6..5....3..5....6..5....5..4....3..6....6..4....3..4....5..6
...
..1..4....1..4....2..1....2..1....2..1....2..1....2..1....2..1....2..1....2..1
..3..2....5..2....4..3....4..3....4..6....3..4....3..4....3..6....5..4....5..3
..6..5....3..6....5..6....6..5....3..5....5..6....6..5....5..4....3..6....6..4
...
..2..1....2..4....2..4....2..4....3..1....3..1....3..1....3..2....3..2....3..2
..5..6....1..3....1..3....1..6....4..2....4..2....5..2....1..4....1..4....1..6
..3..4....5..6....6..5....3..5....5..6....6..5....6..4....5..6....6..5....5..4
...
..3..4....3..4
..1..2....1..2
..5..6....6..5
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..210 (first 180 terms from R. H. Hardin)

Crossrefs

Columns k=1-10 give: A000045(n+1), A006253, A028447, A028448, A028449, A028450, A028451, A287052, A287053, A287054.

Main diagonal gives A181205.