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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 Fan Chung, R. L. Graham, Primitive juggling sequences, Am. Math. Monthly 115 (3) (2008) 185-19 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)]); MATHEMATICA LinearRecurrence[{4}, {1, 2, 6}, 30] (* Harvey P. Dale, Aug 23 2018 *) 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 October 16 04:02 EDT 2018. Contains 316259 sequences. (Running on oeis4.)