|
%I #16 Jul 29 2017 13:28:15
%S 3,3,3,4,2,3,3,3,3,4,2,4,2,3,4,4,1,5,2,2,5,3,1,3,3,3,3,3,3,4,2,3,4,2,
%T 3,3,4,4,1,3,5,2,2,3,5,3,1,4,2,3,3,4,2,4,2,4,4,1,3,4,4,4,0,4,5,1,2,4,
%U 5,3,0,5,2,2,3,5,2,4,1,5,3,1,3,5,3,4,0,5,5,1,1,5,5,2,0,6,2,2,2,6,2,3,1,6,3
%N An infinite juggling sequence of three balls: successively larger ground-state 3-ball site swaps listed in lexicographic order.
%C Every possible 3-ball asynchronic site swap of finite period occurs as a subsequence of this sequence. E.g., "51" (three-ball shower) occurs first time at a(65)=5, a(66)=1.
%C We obtain the sequence by traversing each possible loop of successively larger lengths in 3-ball state graph as depicted in Polster's book, or section 7 of Knutson's Siteswap FAQ (but not limited by throw height), starting from and ending to the ground state 7 (xxx) and by concatenating those sequences in lexicographic order.
%C One can take any subsequence A084501[i..j] such that A084503(i-1) = A084503(j) = 7 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 first 39 terms, one gets a site swap pattern "333423333424234415225313333334234233441".
%D B. Polster, The Mathematics of Juggling, Springer-Verlag, 2003, p. 45.
%H A. Karttunen, <a href="/A084501/b084501.txt">Table of n, a(n) for n = 1..283991</a>
%H A. Karttunen, <a href="/A084507/a084507.scm.txt">Scheme-program for computing this sequence</a>
%H A. Knutson, <a href="http://www.juggling.org/help/siteswap/faq.html#deep">Siteswap FAQ, Section 7, A deeper level: landing schedules, or juggling states</a>
%H Juggling Information Service, <a href="http://www.juggling.org/programs/">Site Swap animators and other juggling software</a>
%H <a href="/index/J#Juggling">Index entries for sequences related to juggling</a>
%e The successive site swaps are: 3; 3,3; 4,2; 3,3,3; 3,4,2; 4,2,3; 4,4,1; 5,2,2; 5,3,1; 3,3,3,3; ... See A084502.
%Y Subsets: A084511, A084521.
%Y The number of such site swaps of length n is given by A084509.
%Y First position where n appears: A084507.
%K nonn,tabf
%O 1,1
%A _Antti Karttunen_, Jun 02 2003
|
