

A084501


An infinite juggling sequence of three balls: successively larger groundstate 3ball site swaps listed in lexicographic order.


11



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, 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, 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
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OFFSET

1,1


COMMENTS

Every possible 3ball asynchronic site swap of finite period occurs as a subsequence of this sequence. E.g., "51" (threeball shower) occurs first time at a(65)=5, a(66)=1.
We obtain the sequence by traversing each possible loop of successively larger lengths in 3ball 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.
One can take any subsequence A084501[i..j] such that A084503(i1) = 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".


REFERENCES

B. Polster, The Mathematics of Juggling, SpringerVerlag, 2003, p. 45.


LINKS

A. Karttunen, Table of n, a(n) for n = 1..283991
A. Karttunen, Schemeprogram for computing this sequence
A. Knutson, Siteswap FAQ, Section 7, A deeper level: landing schedules, or juggling states
Juggling Information Service, Site Swap animators and other juggling software
Index entries for sequences related to juggling


EXAMPLE

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.


CROSSREFS

Subsets: A084511, A084521.
The number of such site swaps of length n is given by A084509.
First position where n appears: A084507.
Sequence in context: A069239 A010265 A239963 * A198020 A098037 A079108
Adjacent sequences: A084498 A084499 A084500 * A084502 A084503 A084504


KEYWORD

nonn,tabf


AUTHOR

Antti Karttunen, Jun 02 2003


STATUS

approved



