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A084501 An infinite juggling sequence of three balls: successively larger ground-state 3-ball 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

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.

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".

REFERENCES

B. Polster, The Mathematics of Juggling, Springer-Verlag, 2003, p. 45.

LINKS

A. Karttunen, Table of n, a(n) for n = 1..283991

A. Karttunen, Scheme-program 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

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Last modified December 15 03:08 EST 2017. Contains 296020 sequences.