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%I #15 May 20 2017 17:59:04
%S 1,2,2,3,9,3,5,32,32,5,8,121,229,121,8,13,450,1845,1845,450,13,21,
%T 1681,14320,32000,14320,1681,21,34,6272,112485,535229,535229,112485,
%U 6272,34,55,23409,880163,9049169,19114420,9049169,880163,23409,55,89,87362
%N 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.
%C Also, the number of perfect matchings in the graph P_2 X P_k X P_n. - _Andrew Howroyd_, May 17 2017
%H Alois P. Heinz, <a href="/A181206/b181206.txt">Table of n, a(n) for n = 1..210</a> (first 180 terms from R. H. Hardin)
%e Table starts:
%e ..1......2.........3............5................8..................13
%e ..2......9........32..........121..............450................1681
%e ..3.....32.......229.........1845............14320..............112485
%e ..5....121......1845........32000...........535229.............9049169
%e ..8....450.....14320.......535229.........19114420...........692276437
%e .13...1681....112485......9049169........692276437.........53786626921
%e .21...6272....880163....152526845......24972353440.......4161756233501
%e .34..23409...6895792...2573281769.....901990734650.....322462050747008
%e .55..87362..54003765..43402320448...32567565264292...24976513162427653
%e .89.326041.422983905.732106008249.1176040842289105.1934824269280528177
%e ...
%e All solutions for 3X2
%e ..1..2....1..2....1..2....1..2....1..2....1..2....1..2....1..2....1..2....1..4
%e ..3..4....4..3....4..3....4..6....3..4....3..6....5..4....5..3....5..6....3..2
%e ..5..6....5..6....6..5....3..5....6..5....5..4....3..6....6..4....3..4....5..6
%e ...
%e ..1..4....1..4....2..1....2..1....2..1....2..1....2..1....2..1....2..1....2..1
%e ..3..2....5..2....4..3....4..3....4..6....3..4....3..4....3..6....5..4....5..3
%e ..6..5....3..6....5..6....6..5....3..5....5..6....6..5....5..4....3..6....6..4
%e ...
%e ..2..1....2..4....2..4....2..4....3..1....3..1....3..1....3..2....3..2....3..2
%e ..5..6....1..3....1..3....1..6....4..2....4..2....5..2....1..4....1..4....1..6
%e ..3..4....5..6....6..5....3..5....5..6....6..5....6..4....5..6....6..5....5..4
%e ...
%e ..3..4....3..4
%e ..1..2....1..2
%e ..5..6....6..5
%Y Columns k=1-10 give: A000045(n+1), A006253, A028447, A028448, A028449, A028450, A028451, A287052, A287053, A287054.
%Y Main diagonal gives A181205.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Oct 10 2010
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