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%I #8 Apr 30 2014 01:29:19
%S 0,1,1,2,3,3,3,4,5,5,5,6,7,7,7,8,9,9,9,10,11,11,11,12,13,13,13,14,15,
%T 15,15,16,17,17,17,18,19,19,19,20,21,21,21,22,23,23,23,24,25,25,25,26,
%U 27,27,27,28,29,29,29,30,31,31,31,32,33,33,33,34,35,35,35,36,37,37,37
%N Maximum mean distance between cards during perfect faro shuffles, with cut, to return to original order in A024222.
%F Take difference between successive cards after each shuffle. Compute mean (if necessary, round to nearest integer). Retain until replaced by a higher mean in a succeeding shuffle.
%F (1/4) {2n + 2 - (-1)^[n/2] + (-1)^[(n-1)/2] }. - _Ralf Stephan_, Jun 10 2005
%F a(n)=A004525(n), n>1. [From _R. J. Mathar_, Oct 15 2008]
%e Consider n=6. There are 4 shuffles to return to original order in a 6-card deck. The maximum mean distance between cards during these 4 shuffles and cuts, s1-s4, is 3, computed as follows: s1, 415263, cut, 263415; s2, 421653, cut 653421; s3, 462513, cut 513462; s4, 456123, cut, 123456. Mean distances: s1 15/5=3, maximum; s2 7/5=1.4; s3 13/5=2.6; s4 5/5; mean cumulative distance: 40/20=2.
%Y Cf. A024222, A024542.
%K easy,nonn
%O 1,4
%A _Enoch Haga_
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