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A048200 Minimal length pair-exchange / set-rotate sequence to reverse n distinct ordered elements. 3
0, 1, 2, 4, 10, 15, 23, 32, 42, 55, 67, 84 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

"Rotate" is always a left-rotate (moves leftmost element to the right end) and "Exchange" is always a pair-exchange of the two leftmost elements.

LINKS

Table of n, a(n) for n=1..12.

Danilo Bazzanella, Antonio Di Scala, Simone Dutto, and Nadir Murru, Primality tests, linear recurrent sequences and the Pell equation, arXiv:2002.08062 [math.NT], 2020.

Sean A. Irvine, Java program (github)

Sai Satwik Kuppili, C++ program for generating the moves for a given n

Sai Satwik Kuppili and Bhadrachalam Chitturi, Exact upper bound for sorting R_n with LE, University of Texas at Dallas (2019).

Sai Satwik Kuppili and Bhadrachalam Chitturi, An upper bound for sorting R_n with LRE, arXiv:2002.07342 [cs.DS], 2020.

Sai Satwik Kuppili and 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^2-10*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: A351927 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 and Srinath T, Bhadrachalam Chitturi, Jan 02 2019

a(12) from Sean A. Irvine, Jun 04 2021

STATUS

approved

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Last modified September 30 21:21 EDT 2022. Contains 357106 sequences. (Running on oeis4.)