A260745 Number of prime juggling patterns of period n using 3 balls.

1, 3, 11, 36, 127, 405, 1409, 4561, 15559, 50294, 169537, 551001, 1835073, 5947516, 19717181, 63697526, 209422033, 676831026, 2208923853, 7112963260, 23127536979, 74225466424, 239962004807, 768695233371, 2473092566267, 7896286237030, 25316008015581, 80572339461372

Offset

1,2

Comments

A juggling pattern is prime if the closed walk corresponding to the pattern in the juggling state graph is a cycle.

Links

Table of n, a(n) for n=1..28.

Esther Banaian, Steve Butler, Christopher Cox, Jeffrey Davis, Jacob Landgraf and Scarlitte Ponce, Counting prime juggling patterns, arXiv:1508.05296 [math.CO], 2015.

Jack Boyce, jprime program, 2024.

Fan Chung and R. L. Graham, Primitive juggling sequences, American Mathematical Monthly 115 (2008), 185-194.

Example

In siteswap notation, the prime juggling pattern(s) of length one is 3; of length two are 42, 51 and 60; of length three are 441, 522, 531, 450, 612, 630, 360, 711, 720, 801 and 900.

Crossrefs

Cf. A260744, A260746, A260752.

Sequence in context: A017938 A333760 A100068 * A119213 A068644 A286318

Adjacent sequences: A260742 A260743 A260744 * A260746 A260747 A260748

Keyword

nonn,more

Author

Esther Banaian, Jul 30 2015

Extensions

a(14)-a(17) from Roman Berens, Mar 20 2021

a(18)-a(28) from Jack Boyce, May 31 2024

Status

approved