A260746 Number of prime juggling patterns of period n using 4 balls.

1, 4, 19, 83, 391, 1663, 7739, 33812, 153575, 677901, 3075879, 13586581, 61458267, 272367077, 1228519987, 5456053443, 24547516939, 109153816505, 490067180301, 2180061001275, 9772927018285, 43467641569472

Offset: 1

Author

Jacob Landgraf, Jul 30 2015

Keywords

• nonn
• more

Comments

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

Examples

			In siteswap notation, the prime juggling pattern(s) of length one is 4; of length two are 53, 62, 71 and 80; of length three are (11)01, (12)00, 660, 750, (10)11, (10)20, 390, 831, 822, 471, 561, 741, 723, 633, 642, 552, 912, 930 and 480.
		

Links

• 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.

Crossrefs

Cf. A260744, A260745, A260752.

Extensions

a(14) from Roman Berens, Mar 20 2021

a(15)-a(22) from Jack Boyce, May 31 2024