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A048200
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Minimal length pair-exchange / set-rotate sequence to reverse n distinct ordered elements.
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3
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0, 1, 2, 4, 10, 15, 23, 32, 42, 55, 67, 84
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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"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.
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LINKS
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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.
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FORMULA
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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
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EXAMPLE
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a(4) = 4 since "xrrx" is the shortest sequence reversing "ABCD". Explicitly, (begin) ABCD, (x)-> BACD, (r)-> ACDB, (r) -> CDBA, (x)-> DCBA.
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CROSSREFS
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Sequence in context: A351927 A333619 A128513 * A058201 A000947 A125245
Adjacent sequences: A048197 A048198 A048199 * A048201 A048202 A048203
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KEYWORD
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nonn,nice,more
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AUTHOR
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Tony Bartoletti
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EXTENSIONS
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a(11) added by Sai Satwik Kuppili and Srinath T, Bhadrachalam Chitturi, Jan 02 2019
a(12) from Sean A. Irvine, Jun 04 2021
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STATUS
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approved
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