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A181206
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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.
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11
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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
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OFFSET
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1,2
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COMMENTS
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Also, the number of perfect matchings in the graph P_2 X P_k X P_n. - Andrew Howroyd, May 17 2017
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LINKS
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EXAMPLE
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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
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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
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..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
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..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
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..3..4....3..4
..1..2....1..2
..5..6....6..5
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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