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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 (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..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^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: 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

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Last modified January 28 09:53 EST 2021. Contains 340490 sequences. (Running on oeis4.)