A115755 Number of permutations of n elements whose unsigned reversal distance is k.

1, 1, 1, 1, 3, 2, 1, 6, 15, 2, 1, 10, 51, 56, 2, 1, 15, 127, 390, 185, 2, 1, 21, 263, 1562, 2543, 648, 2, 1, 28, 483, 4635, 16445, 16615, 2111, 2, 1, 36, 820, 11407, 69863, 169034, 105365, 6352, 2

Offset

1,5

Comments

Probably an erroneous version of A300003. Some inner terms of the triangle differ slightly. Sean A. Irvine reread the paper and checked manually that a(13) should be 52. The last row 1, 36, 820 ... 6352, 2 was added later and is ok. - Georg Fischer, Feb 24 2020

Links

Table of n, a(n) for n=1..45.

J. D. Kececioglu, and D. Sankoff, Exact and approximation algorithms for sorting by reversals, with application to genome rearrangement, Algorithmica (1995) 13:180.

Example

a(3,1) = 3 because the only three permutations of S_3 that require exactly one reversal to be sorted are (1 3 2), (2 1 3) and (3 2 1).

Crossrefs

Cf. A300003.

Sequence in context: A143778 A200536 A164645 * A300003 A259879 A016556

Adjacent sequences: A115752 A115753 A115754 * A115756 A115757 A115758

Keyword

nonn,tabl

Author

Anthony Labarre, Mar 29 2006, Jun 03 2006

Status

approved