

A048200


Minimal length pairexchange / setrotate sequence to reverse n distinct ordered elements.


3



0, 1, 2, 4, 10, 15, 23, 32, 42, 55, 67
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OFFSET

1,3


COMMENTS

"Rotate" is always a leftrotate (moves leftmost element to the right end) and "Exchange" is always a pairexchange of the two leftmost elements.


LINKS

Table of n, a(n) for n=1..11.
Danilo Bazzanella, Antonio Di Scala, Simone Dutto, Nadir Murru, Primality tests, linear recurrent sequences and the Pell equation, arXiv:2002.08062 [math.NT], 2020.
Sai Satwik Kuppili, C++ program for generating the moves for a given n
Sai Satwik Kuppili, Bhadrachalam Chitturi, Exact upper bound for sorting R_n with LE, University of Texas at Dallas (2019).
Sai Satwik Kuppili, Bhadrachalam Chitturi, An upper bound for sorting R_n with LRE, arXiv:2002.07342 [cs.DS], 2020.
Sai Satwik Kuppili, Bhadrachalam Chitturi, Exact upper bound for sorting R_n with LE, Discrete Mathematics, Algorithms and Applications, 2020.


FORMULA

Conjecture: a(n) = (3*n^2/4)2*n if n is even and a(n) = (3*n^210*n+15)/4 if n is odd. See links for more information.  Sai Satwik Kuppili and Bhadrachalam Chitturi, Jun 09 2020


EXAMPLE

a(4) = 4 since "xrrx" is the shortest sequence reversing "ABCD". Explicitly, (begin) ABCD, (x)> BACD, (r)> ACDB, (r) > CDBA, (x)> DCBA.


CROSSREFS

Sequence in context: A217134 A333619 A128513 * A058201 A000947 A125245
Adjacent sequences: A048197 A048198 A048199 * A048201 A048202 A048203


KEYWORD

nonn,nice,more


AUTHOR

Tony Bartoletti


EXTENSIONS

a(11) added by Sai Satwik Kuppili, Srinath T, Bhadrachalam Chitturi, Jan 02 2019


STATUS

approved



