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A084509 Number of ground-state 3-ball juggling sequences of period n. 10
1, 2, 6, 24, 96, 384, 1536, 6144, 24576, 98304, 393216, 1572864, 6291456, 25165824, 100663296, 402653184, 1610612736, 6442450944, 25769803776, 103079215104, 412316860416, 1649267441664, 6597069766656, 26388279066624 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence counts the length n asynchronic site swaps given in A084501/A084502.

Equals row sums of triangle A145463. - Gary W. Adamson, Oct 11 2008

REFERENCES

B. Polster, The Mathematics of Juggling, Springer-Verlag, 2003, p. 48.

LINKS

Table of n, a(n) for n=1..24.

Fan Chung, R. L. Graham, Primitive juggling sequences, Am. Math. Monthly 115 (3) (2008) 185-19

Index entries for sequences related to juggling

Index entries for linear recurrences with constant coefficients, signature (4).

FORMULA

a(n) = n! for n <= 4, a(n) = 6*4^(n-3) = A002023(n-3) for n >= 3.

G.f.: x(1-2x-2x^2)/(1-4x). - Philippe Deléham, Aug 16 2005

MAPLE

A084509 := n -> `if`((n<4), n!, 6*(4^(n-3)));

INVERT([seq(A084519(n), n=1..12)]);

CROSSREFS

First differences of A084508. INVERT transform of A084519. Cf. also A084529.

Cf. A145463. - Gary W. Adamson, Oct 11 2008

Sequence in context: A179350 A179356 A179363 * A147915 A147906 A147898

Adjacent sequences:  A084506 A084507 A084508 * A084510 A084511 A084512

KEYWORD

nonn,easy

AUTHOR

Antti Karttunen, Jun 02 2003

STATUS

approved

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Last modified December 14 21:33 EST 2017. Contains 296020 sequences.