%I #45 Jun 05 2021 16:42:03
%S 0,1,2,4,10,15,23,32,42,55,67,84
%N Minimal length pair-exchange / set-rotate sequence to reverse n distinct ordered elements.
%C "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.
%H Danilo Bazzanella, Antonio Di Scala, Simone Dutto, and Nadir Murru, <a href="https://arxiv.org/abs/2002.08062">Primality tests, linear recurrent sequences and the Pell equation</a>, arXiv:2002.08062 [math.NT], 2020.
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a048/A048200.java">Java program</a> (github)
%H Sai Satwik Kuppili, <a href="/A048200/a048200_1.cpp.txt">C++ program for generating the moves for a given n</a>
%H Sai Satwik Kuppili and Bhadrachalam Chitturi, <a href="https://cs.utdallas.edu/wp-content/uploads/2019/09/LE.pdf">Exact upper bound for sorting R_n with LE</a>, University of Texas at Dallas (2019).
%H Sai Satwik Kuppili and Bhadrachalam Chitturi, <a href="https://arxiv.org/abs/2002.07342">An upper bound for sorting R_n with LRE</a>, arXiv:2002.07342 [cs.DS], 2020.
%H Sai Satwik Kuppili and Bhadrachalam Chitturi, <a href="https://doi.org/10.1142/S1793830920500330">Exact upper bound for sorting R_n with LE</a>, Discrete Mathematics, Algorithms and Applications, 2020.
%F 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
%e a(4) = 4 since "xrrx" is the shortest sequence reversing "ABCD". Explicitly, (begin) ABCD, (x)-> BACD, (r)-> ACDB, (r) -> CDBA, (x)-> DCBA.
%K nonn,nice,more
%O 1,3
%A _Tony Bartoletti_
%E a(11) added by _Sai Satwik Kuppili_ and Srinath T, _Bhadrachalam Chitturi_, Jan 02 2019
%E a(12) from _Sean A. Irvine_, Jun 04 2021
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