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A084511 An infinite juggling sequence of three balls: successively larger indecomposable ground-state 3-ball site swaps listed in lexicographical order. A subset of A084501. 13

%I #9 Jul 29 2017 13:28:36

%S 3,4,2,4,4,1,5,2,2,5,3,1,4,4,4,0,4,5,1,2,4,5,3,0,5,2,4,1,5,3,4,0,5,5,

%T 1,1,5,5,2,0,6,2,2,2,6,2,3,1,6,3,1,2,6,3,3,0,6,4,1,1,6,4,2,0,4,4,5,0,

%U 2,4,5,1,4,1,4,5,5,0,1,4,6,1,2,2,4,6,1,3,1,4,6,3,0,2,4,6,4,0,1,5,2,4,4,0,5

%N An infinite juggling sequence of three balls: successively larger indecomposable ground-state 3-ball site swaps listed in lexicographical order. A subset of A084501.

%C By "indecomposable" we mean that the juggling state sequence associated to each loop should not return to the ground state 7 (xxx) until after the last throw. I.e., this means that A084515 gives positions of ALL the 7s (ground states) in A084513.

%C One can take any subsequence A084511[A084515(i)+1..A084515(j)] (j>i) and try to juggle it periodically or give it to one of the Siteswap animators available at J.I.S., e.g., by taking the terms 4-12, one gets a site swap pattern "441522531".

%H Juggling Information Service, <a href="http://www.juggling.org/programs/">Site Swap animators and other juggling software</a>

%H A. Karttunen, <a href="/A084507/a084507.scm.txt">Scheme-program for computing this sequence</a>

%H <a href="/index/J#Juggling">Index entries for sequences related to juggling</a>

%e The successive site swaps are: 3; 4,2; 4,4,1; 5,2,2; 5,3,1; 4,4,4,0; 4,5,1,2; 4,5,3,0; ... See A084512.

%Y Subset: A084521.

%Y The number of such site swaps of length n is given by A084519.

%Y First position where n appears: A084517.

%K nonn,tabf

%O 1,1

%A _Antti Karttunen_, Jun 02 2003

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